The Reds have come back strongly from a disappointing start to the campaign and are currently ninth in the league table.
That position sees them just four points off fifth placed Spurs and six points behind fourth-placed Arsenal.
Key to their resurgence has been appointing Jurgen Klopp as the manager, and Keown believes the German can get them into the Champions League.
“I do think Klopp has made the Champions League a real possibility for Liverpool and they will be battling it out with Tottenham,” he told the Daily Mail.
“The German has been able to work his magic quickly and actually the 0-0 in his first game at Tottenham looks like a good result for them.”
“His team’s performances are starting to match his ideas. It was a wonderful performance against Man City and even though it’s only one game, Klopp creates such energy.”
Given how poorly Liverpool started the season, it is hard to imagine touting them as top-four candidates.
However, things have considerably improved under former Borussia Dortmund coach Klopp, with them now looking like a dangerous outfit under the German.
Nowhere has the improvement been more noticeable than up front, with the display against Manchester City demonstrating their ability going forward.
Competition will be fierce for that top-four place, though, and given Spurs are unbeaten since the opening day, it is hard to bet against them this season.
There are also several outside contenders, with the likes of Everton, Southampton and Leicester City sure all to be eyeing the top four as well.