Mr Galloway has not commented on the invitation, or Mr Freer’s comments.
Two years ago he walked out of a debate at Oxford University after discovering his opponent was Israeli, saying “I don’t debate with Israelis”.
Earlier this month Mr Galloway interviewed Israeli antisemite Gilad Atzmon on his Russia Today television show.
Other panellists announced so far for the February 5 edition of Question Time are Labour’s Shadow Education Secretary Tristram Hunt and journalist Janet Street-Porter.
A BBC spokesperson said: "Question Time invites panellists who reflect a significant range of opinions on a number of different topics. Whilst Mr Galloway’s views are entirely his own, as an MP he has a right to appear on the programme and has done so previously.
"Subjects for discussion are chosen by our audience ahead of each show and this edition of Question Time will be no different.”
