The 26-year-old joined the Bundesliga champions from Real Madrid on a two-year loan deal at the start of the season, and the German side are reportedly eager to make the move permanent.
James has established himself as an important member of manager Jupp Heynckes' team and has now backed them to win the Champions League. They will host Besiktas in the first leg of their last-16 tie next week.
"Bayern is my favourite to win the Champions League," James told Sport Bild.
"We have a super team with top players. Why shouldn't we win the Champions League?"
The Colombian has played in 24 games for Bayern across all competitions this campaign and has scored four goals and made six assists in that time.
He was part of the Real Madrid side that knocked Bayern out of the Champions League at the quarter-final stage of the competition last season.