Mick Jagger has reportedly been asked to play
Several Sunday newspapers have said the stars will play together in a "supergroup", joined by Phil Collins, Aretha Franklin, Stevie Wonder and Bryan Adams.
Neither Buckingham Palace nor the BBC, who will broadcast the event, would confirm the reports, saying an official announcement would not be made until 12 February.
The concert will be watched live by 14,000 people in the palace gardens, with big screens outside the palace gates, and by millions more on BBC TV and radio.
The concert would be the first time former Beatles guitarist McCartney and Rolling Stones singer Jagger had performed together on stage.
The newspaper said former Beatles producer Sir George Martin was putting together the line-up with respected United States producer Phil Ramone.
The concert would be a "funky yet traditional" event, a Palace spokesperson was quoted as saying.
According to the newspaper, a BBC spokesperson said: "Sir Paul, Mick Jagger, Phil Collins and the others have all been approached and the plan is to create interesting collaborations.
"We will also have collaborations between old and young. The idea is to have the best of British music and use it in different ways."
Aretha Franklin has already issued a statement saying she would take up her invitation to play.
The Sunday Times say Sir Elton John and Robbie Williams will also be on the list of performers.
There were fears that public apathy for the Jubilee could dampen the celebrations.
The concert will take place on 3 June - one day after the 50th anniversary of the Queen's coronation.
A classical concert will be held in Buckingham Palace's grounds on 1 June.
It will be the first time the Palace grounds, usually the venue for invitation-only Royal garden parties, are opened for public concerts.
Tickets will be issued through a free ballot.