The 25-year-old, who used to play alongside new Gers boss Steven Gerrard at Anfield, is available on a free transfer after being released by the Reds in June.
A number of newspaper reports have claimed that Flanagan has had a medical and is set to join up with the rest of the Rangers squad, who are currently in Spain for a pre-season training camp.
"We know Flanagan pretty well," McAllister told STV. "Steven has played alongside him, he's a strong character and the big thing is that he's played for a club where the expectation is so high.
"That's not dissimilar to Rangers, where that expectation is still there. You are under the microscope every minute of every game, so we're confident he can cope with that. He's versatile across the back line, he'll bring a lot."
Flanagan made 51 appearances for Liverpool during eight years at the club.