Hanvey, the MP for Kirkcaldy and Cowdenbeath, won his seat from Labour at the general election in December despite being disowned by the SNP after posting material from the Russian news website Sputnik.
One post is understood to have included a cartoon of Hungarian billionaire George Soros, who is Jewish, controlling puppets of world leaders.
Hanvey issued an apology for his “dreadful errors of judgment” and said he supported the SNP national executive’s decision to suspend him.
However, he has continued to sit with his SNP colleagues on the Commons benches since being sworn in. This week he was pictured taking part in a protest against English Votes for English Laws in the voting lobbies.
“I would expect him to be let off with a slap on the wrist,” a source said. “He’s been contrite and done all the right things. There isn’t that much to investigate.”
The source suggested Hanvey may be readmitted while attention is focused on the upcoming trial of former First Minister Alex Salmond.
A number of SNP members defied a party edict not to campaign for Hanvey in the election, and last month the MP was backed to return by his constituency party, which expressed its “full confidence in, and support for” him.
In a letter to the SNP national executive, local members called for “an urgent end” to Hanvey’s suspension “so that he can fully represent us as the SNP MP, thus reflecting the expressed wishes of his electorate”.
Scottish Conservative chief whip Maurice Golden said: “The SNP has taken the people of Scotland for fools on this matter.
“On paper he’s suspended, but in every other measure of practice he’s very much one the gang.
“The SNP’s sanctioning of someone committing anti-semitic rhetoric was insincere, and it looks like they’re just not serious about his offences.”
An SNP spokesperson said: “It would be inappropriate to comment while disciplinary action is ongoing.”