The 47-year-old is said to be discussing the possibility of portraying the late Beatles star, who was shot dead by Mark Chapman in 1980 aged 40, in a new movie about his life.
Pitt is meant to be a big fan of Lennon's music and is allegedly planning to produce the film as well as act in it.
And Brad has also apparently won over John's widow Yoko Ono.
An insider told British newspaper The Daily Express: 'Brad already has a writer working on the script. And Yoko has given the project her blessing so long as it's true to John's life.
'Brad wants to do all the singing himself and plans to take voice lessons. If he can't pull it off they'll use John's own voice.'
The source added: 'Brad has also been immersing himself in videos and books so he can get Lennon's mannerisms down pat.'