Ancelotti is already under pressure after seeing his side suffer a surprise 2-0 defeat to Hoffenheim on the weekend.
And Basler, who left Bayern in 1999 after a three-year stint, believes that the Italian may have already manufactured an exit strategy.
"I have been told that Ancelotti has signed with a Chinese club," he told German talk show Sport1.
"From what I understand, he could leave as soon as January because that is when the season in China starts."
Basler's claim appears to rest on the reliability of his source, but the former Germany international is confident that his information is accurate.
"I cannot confirm it 100 per cent but my source is very trustworthy," he added. "I can't say anything negative about my source, who I trust completely.
"I'm not saying it's definitely true, but this is what I've been told."
Meanwhile, one of Ancelotti's former players admits that the former AC Milan coach may struggle to meet expectations at Bayern.
Ancelotti led Bayern to the Bundesliga title in his first season but Paolo Maldini - his captain at AC Milan from 2001 to 2009 - said winning the UEFA Champions League might be an unrealistic goal.
Maldini told Bild: "He is a great man. I don't know if he can show it in Germany.
"What they want from you at Bayern is the Champions League. And that is not self-evident. It is possible but it won't be easy."