The Genius Media Nigeria reports that Leicester boss Rodgers is now favourite after the extra time defeat to Everton in the FA Cup.
Rodgers is followed by Julian Nagelsmann, Eddie Howe and Max Allegri with Scott Parker and Rafa Benitez also in the running, according to Betfair.
Southampton boss Ralph Hassenhuttl had been second favourite at 5/1, but is no longer in the mix according to Betfair’s market.
Mourinho is now the 2/1 favourite to be the next Premier League manager sacked.
Tottenham were dumped out of the FA Cup last night by Everton and face Premier League leaders Manchester City on Saturday.
They did beat West Brom 2-0 at the weekend to keep their European hopes alive, but had lost three Premier League games in a row before that.
Mourinho’s sides are usually resolute defensively however conceding five to Everton showcased more problems within his team.
And the Portuguese lamented the mistakes made but said he was pleased with their attacking play.
Mourinho told BT Sport after the game: “I enjoyed it, and I didn’t enjoy it. I enjoyed the way we played when we had the ball, from the first minute, immediately. We scored four goals and four goals was not enough.
“If it hurts me [the lack of defending], it hurts everyone from our team because the feeling is that we played really well, when we had the ball we were brave, we created.