The former midfielder Jenas was seen by many bookmakers as the favourite to replace Lineker when he eventually steps down.
However, he has been sacked from Match of the Day and the One Show, effectively ending his hopes of succeeding Lineker.
Lineker has presented Match of the Day since 1999, with his current contract set to expire at the end of the current season.
It's understood the complaints regarding Jenas related to his 'workplace conduct' and that the issues were raised with the broadcaster a few weeks ago, and it took action.
A new favourite to replace Gary Lineker (pictured) as Match of the Day host has emerged
According to The Times, Mark Chapman is now the frontrunner to replace Lineker as the new presenter of the iconic programme.
Chapman has landed the role of lead presenter for BBC's new Champions League highlights show, with the 50-year-old set to start his new role next week.
The BBC secured the rights in a three-year deal with UEFA that will return the Champions League to terrestrial channels.
The same outlet claims that is the reason why Chapman will be the favourite to become the new MOTD host from next season.
Chapman currently hosts Match of the Day 2 and has done since 2013 so becoming the face of the show on Saturdays would come as no surprise.
However, it would mean that he gives up his radio work on 5 Live Sport which will likely come as no issue given the huge opportunity ahead of him.
Chapman has worked on various other programmes including Final Score and The NFL Show since joining the BBC in 1996
Gabby Logan, who has often stood in for Lineker on Match of the Day, has also previously been touted as the latter's replacement.