James starred in the 2014 FIFA World Cup and soon joined the Madrid giants who were then coached by Italian Ancelotti.
While James had a fruitful maiden season, he has since fallen down the pecking order under current Madrid chief coach Zinedine Zidane, including this season.
Now, Ancelotti at Bayern has asked the Bavarians to make an effort to bring James to Germany in the summer, according to a report in Spain's Marca newspaper.
"It's a deal that, apparently, has the blessing of the directors of the Bavarian club and it's a move which the Colombian would jump at," Marca published in their website.
It is believed that even though Zidane continues to speak highly of James, he doesn't consider him in his scheme of things and for the 25-year-old Colombian, it will be best if he plays regularly.
For a club as big as five-time European champions Bayern, it would not be hugely difficult to splurge around $80 million to rope in James' services.
But, according to the newspaper, Bayern are not the only club interested in James. Jose Mourinho-coached Manchester United are also looking at him as well as other English clubs such as Chelsea, with star striker Diego Costa's future uncertain.
Record Italian champions Juventus are also interested as the Turin giants aim to return to the top of European football. In the past, Paris Saint-Germain (PSG) have also been linked with the player.