According to the Mail on Sunday, Scissor Sisters frontman Jake Shears met the 'Alejandro' singer at Sir Elton John's White Tie and Tiara Ball in June. The stars have been negotiating the details of the project since the meeting, and are in the final stages of reaching an agreement.
A source told the newspaper: "Jake has performed with huge stars like Kylie (Minogue). He is desperate for the union with Lady GaGa to go ahead.
"He was concerned Lady GaGa might decide against it but he has been reassured that the collaboration will happen in some way, shape or form."
Shears has previously said he is "proud" that the 24-year-old considers the Scissor Sisters to be a musical influence.