Rodgers has banned his players from discussing such possibilities but knows they have boosted their chances after Jamie Vardy’s late goal grabbed a point at Arsenal in midweek, preventing what would have been a third defeat since the re-start.
He said: “Whether you’re winning 3-0 or 4-0 or not, you have to push, so I think it’s a mental attitude that we’re never beaten, we keep pushing whether we’re ahead or losing the game.
“But it’s also down to physicality. We’ve got a really, really good level of fitness in the squad, and that’s testament to how hard they work on a daily basis and the recovery strategy.
“Emotionally with the players we try to get them to push and they continually do that. It’s great to have that in your team, knowing the game’s never over until the last minute.”
But Rodgers has hailed Howe, who is facing arguably his biggest challenge at the club since he stepped in to save them from relegation out of the Football League 11 years ago.
Rodgers said: “I know Eddie and he is an outstanding manager for what he has done for Bournemouth and where he has taken them.
“For me there is no doubt about his ability as a manager – his quality and how hard he works, the consistency that he shows and the types of teams he develops.
“He has done a phenomenal job and it can happen to you if you get a little run like they’re in. But they know they are still in with a fighting chance with four games to go.”
Rodgers has confirmed he will once again be without inspirational pair James Maddison and Ben Chilwell for the trip to the Vitality Stadium due to hip and ankle injuries respectively.