Dr Harry Hagopian shared his concerns with Premier following the police's announcement late on Tuesday that Mr Netanyahu accepted around £200,000 in gifts from two billionaires.
The Prime Minister is also accused of receiving gifts such as champagne and cigars in exchange for helping a Hollywood mogul get a US visa.
While Mr Netanyahu has shrugged off the police recommendations, calling the allegations "biased, extreme, full of holes, like Swiss cheese", Dr Hagopian said the leader should be worried.
"He knows that his premiership is at stake depending on how this whole legal soap opera is played out within the Ministry of Justice and the Prime Minister's office as well as within the Attorney General's offices as well," Dr Hagopian added.
Israeli opposition leaders have called on Mr Netanyahu to step down but the long-time premier has rejected those calls as well.
Nearly all of Mr Netanyahu's Cabinet ministers issued statements of support. Mr Netanyahu's coalition whip, David Amsalem, accused the police of committing "an illegitimate act here to attempt a coup d'etat in Israel".
Commenting on the fact that Mr Netanyahu has been the subject of investigations many times in the past, Dr Hagopian said "there is no smoke without fire".
However, he said changing leaders right now would be a bad idea.
"The two things that worry me at the moment about whether he's indicted or whether he goes to court or whether he might even have to step down as Prime Minister is first the whole region is in turmoil.
"We've just seen what's happened along the Israeli-Syrian border... we know that the Palestinian occupied territories are tense so the change in leadership and that sense of loss of momentum and control would not be such a good thing.
He might go but the big question is "if he were to go who would succeed him and would that be an improvement to where we are today?"
Listen to Dr Harry Hagopian speaking with Premier's Tola Mbakwe:
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