Salah in particular has been linked with a move away from Anfield with Real Madrid supposedly interested.
But Barnes doesn’t think Dembele joining would see Liverpool having to sell one of their star forwards.
“I can’t see a reason for any of the front three to leave because they like it at Liverpool and things are going well,” he added.
“I don’t think there’s a reason any of the front three need to feel they have to leave to fulfil their ambitions because they’ve won the league and the Champions League so it’s hard to say what more they want.
“In terms of the potential to be successful, they won’t get it much better anywhere else, it’s just a question of whether they feel they want a new challenge. Some of them are coming up to 28/29 and sometimes players move on.”