Madonna invited Gaga to perform with her at the Yankee Stadium gig in their native New York last month.
However, Gaga declined the offer as she was too busy on her Born This Way Ball tour to spare the time, reported Sun Online.
"Madonna called to ask Gaga to perform with her at Yankee Stadium. Her manager reached out to us and said Madonna would like Gaga to perform with her," Gaga's manager Vincent Herbert said.
Herbert insists her decision to turn Madonna down had nothing to do with their long-running feud.
"She really wished she could do it. She said, 'If we do it, let's donate the money to charity'. But Gaga's committed to her own tour."
Relations between the two has strained since Gaga released her single 'Born This Way' last year, with Madonna repeatedly comparing it to her 1989 hit 'Express Yourself'.
Onstage in July, Madonna declared herself a huge fan of 'Born This Way' because "she helped to write" the song.
"I love her - imitation is the sincerest form of flattery," Madonna had said.
