The Colombia international is presently in the midst of a two-year spell at the Allianz Arena and has recently won praise for fine displays.
Rummenigge hailed former coach Carlo Ancelotti, who was sacked earlier in the season, for attracting the 26-year-old to the club, but rejected claims that the Bavarians have already decided to buy the former Monaco and Porto star, whose clause is valued at €42 million.
“He has developed excellently, especially since Jupp Heynckes took over. It was a very good transfer and I have to congratulate Carlo Ancelotti again for that,” he said.
“There are clear conditions regarding his contract and we are not in a hurry.”
James is expected to play a crucial role for them, having scored one and set up two in Saturday’s spectacular 6-0 demolition of Borussia Dortmund .
In total, he has played 28 times for Bayern since arriving in the summer and has scored five goals and created another 11.
Meanwhile, Bayern are still on the lookout for a coach to replace Ancelotti on a permanent basis, with a decision expected by the end of the month .