He does, however, have doubts about Arsenal's ability to finish in the top four if Arsene Wenger does not sign a new striker.
The Reds left White Hart Lane with a 3-0 win at Spurs on Sunday, after goals from Raheem Sterling, Steven Gerrard (from the penalty spot) and Alberto Moreno got them back to winning ways.
And the performance was reminiscent of the Liverpool of last season, with the Anfield side playing in a diamond, while Mario Balotelli joined Daniel Sturridge up front.
By contrast, Tottenham looked disjointed for the first time this season after winning their opening two Premier League games.
As such, Lineker believes Rodgers' side must not be underestimated this season, especially due to the Nothern Irishman's tactical knowledge.
Don't underestimate this Liverpool sides chances, especially under the shrewd, tactically astute leadership of Brendan Rodgers.— Gary Lineker (@GaryLineker) August 31, 2014
But Arsenal's 1-1 draw at Leicester City has left Lineker in serious doubt as to the Gunners' ability to finish in the top four.
As for Arsenal, if Wenger doesn't bring in a decent striker even 4th place might elude them this season.— Gary Lineker (@GaryLineker) August 31, 2014
Yaya Sanogo started the game against Leicester but produced another poor display, while Olivier Giroud is out with a broken foot and £35 million summer signing Alexis Sanchez is not a natural centre-forward.
Wenger has one day left to sign a new striker for the north London side.
Do you agree with Lineker's views on Liverpool and Arsenal?