Gallagher is yet to make his first-team debut for Chelsea after being brought through their academy but has impressed during his loan spell at Crystal Palace this season.
Chelsea are yet to make a decision over the 22-year-old’s future but Thomas Tuchel will get a closer look at the midfielder during their pre-season campaign this summer.
But Austin, who has made over 100 Premier League appearances, believes Liverpool should make a move for Gallagher and believes the England international’s energy would be an ideal fit for Jurgen Klopp’s system.
‘I think for any team who are rebuilding would like Conor Gallagher,’ Austin told talkSPORT.
‘He’s so energetic, you look at him the way he plays, the way he carries himself.
‘I think a lot of football fans see him play and think, ‘I’d like him at my football club’. I do believe that.
‘I would say he would be, not a replacement, but Jordan Henderson, I’d put him in there when Jordan moves on, or retires or goes into a different football role, he [Gallagher] would be great.’
Meanwhile, Crystal Palace chairman Steve Parish confirmed last week that the club will attempt to keep Gallagher at Selhurst Park for at least another season.
‘Of course, but the player is the number one person,’ said Parish.
‘He knows exactly what his priorities are and he knows exactly what he’s doing.
‘I’m sure at the end of the season. Conor will work out what he thinks the best thing for him is and that will that will be the catalyst for it.
‘If there’s an opportunity to get him or even Ruben Loftus-Cheek then of course.
‘These are top players and it’s been brilliant having him here this year, not just because of what he does on the pitch. Also because of the way he is around the place, the way he is with the media and supporters and because of how special a lad he is.’
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