An adjective "rumored" definitely seems to exist
The OED has an entry for rumored as an adjective. (It suggests that it was actually originally formed from the noun rumor rather than from the verb.)
To avoid just giving an argument from authority, I'll mention a piece of evidence that indicates that an adjective rumored exists: a word unrumored meaning approximately "not rumored" exists, and the prefix un- that means "not" doesn't attach to verbs, only to adjectives. (A separate prefix un- exists that attaches to verbs, but it has a "reversative" meaning.) Here's a quote from a Business Insider article that provides an example of the adjective unrumored:
We could still be surprised, by a heretofore unheard of or unrumored Tesla product
("Here's everything we know about Tesla's big April 30 announcement", by Matthew DeBord, 2015 Apr. 25)
What I'm not sure about is if we are looking at the adjective "rumored" in constructions like "...rumored to be..." and "...rumored that...".
Is "rumored" a verb or an adjective in particular sentences?
Showing that something that looks like a participle is a verb rather than an adjective is actually a bit tricky. The only way I know to demonstrate this for sure is when the word takes a direct object—it seems to be generally agreed that this can only happen with participles/verbs and not with departicipial adjectives.
All of the other tests that I know of are for showing that a word is an adjective, and they don't seem to be conclusive here. From what I have read, a participle-looking word must be an adjective if it is
prefixed with the negative prefix un- (meaning "not", as in "unkind" ≈ "not kind"—not the homonymous reversative prefix un-, as in untangle or unlock, which do not mean "not tangle" and "not lock")
preceded by "how" (as in "How organized is your desk?")
- used after "seem", as in "They seem organized." (BillJ's answer here also mentions "become" and "find" as two other verbs that behave similarly in taking adjectives but not verbs as complements)
Also, the adverb "very" cannot be used by itself before verbs.
To me, none of these tests demonstrate anything conclusive about "rumored" in "rumored to be", because I don't think that I can say "*unrumored to be", "*how rumored to be", "*seem(s) rumored to be", or "*very rumored to be".
"seems rumored to be"?
However, I was able to find some examples of "seems rumored to be" with a Google search, which suggests that some speakers do treat "rumored" as an adjective in this context.
The SV650 looks OK also but its suspension seems rumored to be not so great.
("What's the bike for me?", Adventure Rider Forums, post #9, by
rodr, 2008 Nov 9)
Kameo has been pushed back and it seems rumored to be released on XB2
("So what's the next Rare game to come out", IGN Boards, post #9, by
L8X2H1, 2004 Nov 20)
I was also able to find more than one example of "became rumored to be":
Ever since Las Vegas became rumored to be the destination for an NHL franchise, Murray Craven's name has been part of the equation.
("Murray Craven: 6 Fun Facts", by Dan Marrazza @GoldenKnights / VegasGoldenKnights.com, August 18th, 2016)
So, the vault became rumored to be a treasure trove of wealth
("Can someone explain the ending to me *SPOILERS*", Borderlands – Message Board, GameFAQd, post #6, by
Shaolinz0, 2010 Jan 9)
Prokhorov already has burned through three coaches in two seasons, and that was before he became rumored to be looking to sell the team.
("So, Which New NBA Coach Will Be Fired First?", by Joseph Flynn, 2014 Nov 3)
"seems rumored that"?
The book Studies of Passive Clauses, by Paul Martin Postal (1986), asserts that "rumored that" is ungrammatical in the following sentence:
(iii) It seems obvious/*rumored that he was a spy.
and says that this is evidence that "rumored" is not an adjective in sentences like (ii) b. "It was rumored that he was a Martian" (p. 138).
I personally would agree with the acceptability judgements that Postal reports. Nevertheless, as with "seems rumored to be", Google search turns up a few examples of "seems rumored that":
During 100% throttle from a stop, it seems rumored that PWM engages(where that "rumbling" comes from) and stops PWMing once it starts coasting.
("What does PWM do?", Endless Sphere:
Electric Vehicle and Technology Forums, Post by swbluto » Sep 19, 2008 9:27 pm)
With Shawn seemingly out of the picture, have you heard of anyone on the horizon coming for Alexis (since it seems rumored that Sam's father is going to Anna)?
("Spoiler Gab: June 16-30", The Road to Nowhere, June 28th, 2013, 1:39 am #562)
Non-passive uses of "rumor" where it is obviously a verb
As you mention, there is evidence that "rumor" has been used in contexts where it is clearly a verb. The OED's second definition is for a transitive usage, and it gives some examples where the word could not be an adjective:
1600 Shakespeare Henry IV, Pt. 2 Induct. 33 This haue I rumour'd through the peasant townes.
1649 F. Roberts Clavis Bibliorum (ed. 2) 556 By the chiefe Author thereof, the Lord, rumouring it.
- 1735 Visct. Bolingbroke Lett. Study Hist. (1777) iv. 96 Those wretched Christians who returned from those wars..rumoured these stories about the West.
- 1811 H. Grattan Let. June in Mem. (1846) V. xii. 442 To-day they rumour that he is not so well, but that he will soon recover, and resume.
- 2009 K. Homewood et al. Staying Maasai? vii. 293 Local people rumoured that Graphtan served as a front for a Tanzanite smuggling operation.
The OED quotes mentioned in the preceding section seem to make it clear that at some point/for some speakers, a verb "to rumor" has been used (in active as well as passive constructions, and in contexts where it takes a direct object).
However, "to rumor" seems to have fallen out of use for many speakers in the active voice.
The Google searches mentioned earlier in my answer provide some evidence that certain speakers do analyze "rumored" as an adjective in constructions like "rumored to be" and "rumored that". But I didn't get a ton of results when I searched for "seems rumored to be", "became rumored to be", and "seems rumored that", so it seems to me that most speakers probably avoid these usages. It's unclear to me whether that means that "rumored" is still a verb for those speakers, or just an abnormal adjective (there are adjectives that have restricted patterns of usage, like "former").