There is a strong belief that the Rangers boss is primed to return to Anfield as manager, whether it is to replace Jurgen Klopp when he leaves or at a future date.
Gerrard, over three years at Ibrox, has performed very well, taking the team deep in Europe and winning the Scottish Premiership.
However, Barnes, who had a short spell as Celtic boss, believes he would have to “show a longer level of consistency” before being considered.
He told BettingOdds.com: “Of course there are other managers that you would think are better suited, such as Steven Gerrard who has had a very good season at Rangers, but is he going to come to Liverpool off the back of one good year? Of course he would be given time because of his relationship with Liverpool.
“If you were to ask me now, if Jurgen Klopp left Liverpool tomorrow would I think Steven was the man for the job? Probably not because you would want a manager with more experience and is proven at the highest level. He would be given time because he’s Steven Gerrard, but would that be the right thing for Liverpool? Maybe not.
“I’m sure Steven will do really well over the course of his career, but he’s going to have to show a longer level of consistency over a longer period of time before we start linking him with the Liverpool job.”