The former Labour MP revealed who he would have running Question Time when current host, Dimbleby, retires from his current role.
Dimbleby has been hosting the BBC debating show since 1994, with Galloway predicting who could replace the 78-year-old presenter.
Speaking on talkRADIO, the 62-year-old hammered the BBC as he shared his thoughts over the next host.
He said: “Quite a few people have said the North of Ireland commentator, William Crawley, would be a good substitute.
Jeremy Paxman and Andrew Neil were lined up for the Question Time host role by Galloway
“For me, it’s a standout, Andrew Neil and, or Jeremy Paxman should be running BBC Question Time and Any Questions?
“Not because they’re not both right-wing – they are both right-wing – but because they’re fair. They know what they’re talking about.
“Anybody who hasn’t grasped that, hasn’t watched Newsnight since Jeremy Paxman left it.”
Dimbleby joined the BBC as a news reporter after leaving university and has appeared in network programmes since 1962.
David Dimbleby hosting Question Time in Torquay
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Nick Griffin attacks Jack Straw’s father – ‘My father was in the RAF during the second World war while Mr Straw’s father was in prison for refusing to fight Adolf Hitler’.
Andrew Neil has been beastly to me on many occasions
The journalist, who has presented the BBC’s general election programmes since 1979, led Question Time after replacing former host Peter Sissons.
Both Paxman, who left Newsnight in 2014 after presenting it since 1994 and Neil, Daily Politics host, have been linked with the role in the future.
Galloway then shared insight into his own encounters with the fiery presenters as he weighed up who would be best for the role after Dimbleby.
He finished: “Paxman was beastly to me on many occasions.
“Andrew Neil has been beastly to me on many occasions.
“The point is they’re beastly to everyone and know what they’re talking about. That brings out the best in you.”