“Can I persuade you” is not a cliché; that is, it is not “a phrase or expression that is overused or used outside its original context, so that its original impact and meaning are lost. A trite saying; a platitude”. Nor is it “an ad hoc expression invented for this occasion”. Ngrams for Can I persuade you shows that it has occurred many time in many books, although it is more typically the beginning of a question, rather than a question by itself. For example:

Can I persuade you to do that?
Can I persuade you to try one of our local wines?
Can I Persuade You?: The Power of Persuading and Influencing [a book title]

All in all, an ordinary phrase, used in a reasonable way.

“Can I persuade you” is not a cliché; that is, it is not “a phrase or expression that is overused or used outside its original context, so that its original impact and meaning are lost. A trite saying; a platitude”. Nor is it “an ad hoc expression invented for this occasion”. Ngrams for Can I persuade you shows that it has occurred many times in many books, although it is more typically the beginning of a question, rather than a question by itself. For example:

Can I persuade you to do that?
Can I persuade you to try one of our local wines?
Can I Persuade You?: The Power of Persuading and Influencing [a book title]

All in all, an ordinary phrase, used in a reasonable way.