According to ESPN, there is a 'break clause' in the three-year contract Ancelotti signed with Bayern in 2016 that would allow the club to end his time at the Allianz sooner than planned.
The Italian delivered a fifth straight Bundesliga title last season, but failed to oversee progress in the Champions League and a quarter final exit in the DFB Pokal has apparently left him under pressure at the start of his second year in charge.
That and the alleged interest in Hoffenheim coach Julian Nagelsmann, whose team beat Ancelotti's Bayern by a 2-0 score-line at the weekend, points to a potential Ancelotti exit.
If that were to be the case, ESPN claims England would a preferred destination for his next job.
The 58-year-old previously spent two years with Chelsea, guiding the club to a domestic double in his first season. That Chelsea team was the first in the Premier League era to score more than 100 goals in a single season, but Ancelotti was sacked just 12 months later.
It remains to be seen where the former Parma, Juventus, Milan, PSG and Real Madrid coach could go if he did arrive in the Premier League for a second stint. Manchester United and Liverpool were both interested in the past, but both are comfortable in the manager department.
Arsenal is unlikely to be an option after Arsene Wenger signed a new two-year contract at the end of last season. Yet a return to Stamford Bridge, a la Jose Mourinho in 2013, might not be beyond the realms of possibility should Antonio Conte's rumoured frustration grow once more.