The former Reds player is expecting a top four challenge, but not a run at the title just yet.
They have also managed to reach the semi-finals of the Capital One Cup after a 6-1 win over Southampton, with things now looking on the up at Anfield.
With the league the most open it has been in a number of years many believe Liverpool could be title challengers, but Barnes has been more realistic with his expectations.
“Although they can challenge for a top-four finish this season, they are not necessarily going to sign the best players in the world in January,” he told the Mirror.
“In the short term, he may have to bring in players he knows well, and who can respond quickly to what he wants. They are not title contenders yet, and I’m still not getting carried away just because Jurgen Klopp is here.
“Realistically, fourth place is possibly within our grasp and then, depending on who he signs in the summer, he can think about making a major push for the title.”
With the way the league is wide open this season, there is no denying that the top four is well within Liverpool’s reach.
They are currently ninth in the table on 24 points, just five points behind Manchester United in fourth, who have been less than impressive so far.
The title is probably beyond them at this point, with leaders Leicester City now on 35 points, and Arsenal and Manchester City on 33 and 32 respectively.
An 11-point gap is probably too much to make up at this point, although given the way it seems nobody wants to run away with the title this season, it is probably too early to rule Liverpool out altogether.