Rodriguez joined Bayern on a two-year loan deal before the start of the 2017-18 campaign, and the Colombian international has scored twice and provided three assists in 12 Bundesliga appearances this term.
As it stands, James will return to parent club Madrid in 2019, but the 26-year-old has suggested that he wants to join Bayern on a permanent deal.
"At Bayern Munich it's great. For that reason, I can see myself playing here for many years more," James told Sport1.
"Bayern Munich are at the same level as Real Madrid, a club of the highest quality. They always fight for titles and are used to securing them. I really like Munich. It's a bit cold, but I'm adapting well. This is a new life for me and Munich is a fantastic city."
James left Los Blancos last summer after struggling to win a regular spot under Zinedine Zidane.