The presenter is currently working on a documentary about the monarchy, The Sun reports.
He is planning to write to Buckingham Palace to ask for a session with the Queen that he can include in the BBC programme.
"This will be about how she reigns and the inside story of every government since Churchill was Prime Minister," Marr said. "I hope we will be able to talk to members of the family and we will be putting in a request to talk to Her Majesty herself."
The documentary is scheduled to air in 2012, the year of the Queen's Diamond Jubilee.