The midfielder has tipped his old side to secure a top four place despite a disappointing start to the campaign.
Spurs have started the season strongly under Mauricio Pochettino, and are currently unbeaten since the opening day, strengthening their hopes of making the top four.
Liverpool haven’t had quite as strong a start, but are now considered as an outside bet since Jurgen Klopp replaced Brendan Rodgers.
There is certainly a spot open for both sides to take advantage of given Chelsea’s fall from grace this year, and Barnes has backed the Reds to beat Spurs to the top four.
“I think Liverpool will [make the top four],” he told BT Sport.
“Manchester City and Arsenal will be first and second, and Manchester United will drop points. Chelsea can’t finish in the top four, and Tottenham could. It’s a battle between Liverpool and Tottenham and I’ll go with Liverpool.”
Given how both sides have started the season, it is hard to see how Liverpool will finish in the top four this season ahead of Tottenham.
Spurs look like a highly organised side under Pochettino, with them having put in a number of impressive performances in recent weeks.
In contrast, Liverpool are still struggling with the same problems of the last few years, as they struggle to score goals and look suspect defensively.
That surely puts Pochettino’s side ahead of Klopp in the race for fourth, although with so much of the season still to play, there could be a big change between now and the end of the season.