The pair joined the Light Blues on loan earlier this month and Gary Mac insists they want to win.
The Gers number two was 35 when he joined Liverpool so has experienced for himself.
Despite his age, he went on to lift both English cups and the UEFA Cup in 2000/01.
“I was a player who went late to a big club so the age thing doesn’t worry me,” McAllister said, as quoted by the Daily Record.
“It will be thrown at these players the same as it was with me.
“I remember fanzines and things saying, ‘This guy has been a decent player but why are we signing someone who is 35?’ but you go and grasp the moment.
“And the facts are if you go to a club like Rangers or Liverpool then it represents a better chance of winning something and that’s still the big desire here.”
There can be no question that both Davis and Defoe have the ability to shine at Ibrox.
Both players could have a huge say in the title’s destination with the Gers currently level with Celtic.
Gerrard’s side are aiming for the club’s first major trophy since 2011.
With both players coming from Premier League teams, they are in great physical condition.
Neither comes with a reputation for partying or not keeping themself in great shape.
The biggest concern will be their lack of action so far this season.
After spending the week with the squad in Tenerife, both need just need brought up to match fitness..
They could make their debuts this weekend in the Scottish Cup tie with Cowdenbeath on Friday.
If they don’t then Sunday’s friendly with HJK Helsinki will surely see them feature.
Hopefully, they can go on to have a similar impact at Ibrox as McAllister did at Anfield.
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