The former forward does however believe they are good enough to challenge for a top four spot this season.
The Reds recently sacked manager Brendan Rodgers and moved quickly to secure former Borussia Dortmund manager Jurgen Klopp as his replacement.
The German has made a big impact already at Anfield with many having been impressed by his first press conference, in which he stated he believed in four years time they will have won a title under his leadership.
Barnes though, says that the current squad doesn’t have enough star quality, aside from Philippe Coutinho.
“Is this Liverpool team good enough to win the league as it stands? No it’s not,” he told TalkSport.
“Apart from Coutinho, who gives us that star quality in terms of invention an flair, we probably don’t have the quality of other big teams. Are we going to be able to compete with Manchester City and Chelsea with the players we have now?”
The former Anfield star has however backed the Reds new manager to make an instant impact on the side following the international break.
The side have been disappointing so far this season, with just three wins from their eight games, with two of those having been unconvincing victories over both Bournemouth and Stoke.
The arrival of Klopp has got many thinking positive though, and Barnes says they can challenge for the top four because the manager likes powerful teams and Liverpool are just that.
“He can make an instant impact,” added Barnes.
“What we know from the first three games of the season is that this Liverpool team has a lot of energy, they’re fit, strong and physical. We’re a very powerful team, and Klopp likes powerful teams. I think it is good enough for the top four."