The Colombian midfielder joined the Bavarian side from Real Madrid on a two-year loan deal last summer, but is expected to make it a permanent switch.
The 26-year-old has been a key player for Jupp Heynckes' side in their European campaign so far, featuring in all six matches as they finished top of their group, and is preparing for next week's clash with Besiktas in the first leg of their last-16 tie at the Allianz Arena.
And Rodriguez expects the Bundesliga leaders to overcome the Turkish side and go all the way to unseat his parent club as European champions.
"Bayern are my favourites 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?"
James' loan move is expected to be made permanent in the near future. German media reports the league leaders will pay around €6.5 million per season he is on loan there, with a further €42m needed to convince Madrid to let him go.
The former Monaco star has scored four goals and made six assists in 16 appearances in the Bundesliga.