Oink oink might be closest in form in American English. This is the English word for the sound a pig makes, and can be used to mean "greedy" (similarly to the trough idiom, I think). "Oink out", for example, equates to "pig out", meaning overeat or binge (see, for example, The Free Dictionary), and I might say "oink oink" as a humorous admonition to my child if I saw him reaching for yet another donut.
Helpfully for this situation, in the US "oink" also evokes political "pork"1. "Pork barrel" is an idiom for a particular kind of political corruption:
pork barrel: government projects or appropriations yielding rich
patronage benefits (Merriam Webster)
pork 2:
government funds, jobs, or favors distributed by politicians to gain
political advantage (Merriam Webster)
This usage of "oink" is not as widespread as the Italian saying you describe, but I think would be pretty instantly understood in context. Some examples from around the web:
(By Jay Lassiter)
(Article at 100% Fed Up)
If, for example, the highest executives of the nation or of the state
are called, not President X or Governor Y but pig X or pig Y, and if
what they say in campaign speeches is rendered as "oink, oink," this
offensive designation is used to deprive them of the aura of public
servants or leaders who have only the common interest in mind. They
are "redefined" as that which they really are in the minds of the
radicals. (Political Humor: From Aristophanes to Sam Ervin By
Charles E. Schutz, 1977)
1Note that "pig" is also a derogatory term for police, and "oink" can be used to reference police (especially those who abuse their powers), so be sure of your contextual cues when/if using.