Next Wednesday's meeting is scheduled to be a "roundtable discussion on the relationship between the Labour Party and the Jewish community."
It will be chaired by Mr Corbyn - with Ms Formby also in attendance.
But the decision to include a group such as JVL in the discussion is likely to infuriate the Board, the JLC and the JLM.
One source told the JC:"It's Jeremy wanting to look as though he has reached out to everyone he possibly can on this matter.
"And not realising the consequence of his actions."
Mr Corbyn will meet leaders of the Board and the JLC on April 24.
Jonathan Arkush, Board president, and Jonathan Goldstein, JLC chairman have confirmed they will meet Mr Corbyn on Tuesday.
Referring to the "Enough is Enough" demonstration organised by their groups in Parliament Square last month, Mr Arkush and Mr Goldstein wrote in the Observer on Sunday: "Last month’s protest was a necessary moment of catharsis, as painful for Labour as it was for our community, but we cannot now return to 'business as usual'.
