The Beatles legend is hoping the sum - together with an alleged $150 million divorce settlement - will be enough to avoid a court battle with his estranged wife over their three-year-old daughter.
A source told Britain's News of the World newspaper: "Bea means everything to him."
"His fear is that if Heather gets custody then she could make things really difficult for him in the future to have proper contact with Bea."
"He is worried she will slowly cut him out of his daughter's life and he couldn't bear that."
"Paul wants the divorce and custody of Beatrice settled in a one-off transaction."
"He has told Heather, 'I get Beatrice and you get the money.'"
Paul and Heather, 38, previously said they would jointly take care of Beatrice.
The 64-year-old, who is reported to be worth $1.5 billion, is planning to raise Beatrice at his 160-acre Peasmarsh estate in Sussex.
Paul was given a standing ovation by well-wishers supporting him in his divorce from Heather Mills last week.
The musician had been enjoying a quiet meal at New York's Italian eatery Il Gattopardo and was left shocked when the whole restaurant erupted into rapturous applause as he stood up to leave.
One diner showed his support for Paul by shouting: "We are with you all the way Paul!"
