David Cameron wants his former school Eton College to create a state school, it has been reported.
The Prime Minister held a meeting with leading public schools representatives at Downing Street on Thursday about ways to involve them in driving up standards in the state sector.
In an interview with the BBC he insisted his door is open to anyone who can help.
Asked if Eton should get involved, Mr Cameron said: "Yes, I would like all private schools to engage in this agenda and if you look at most private schools, many of them already run bursaries for children from less well-off backgrounds and partnering state schools.
"To me, all private schools have always had a charitable foundation, a charitable purpose, and that's a great way to deliver that."
Mr Cameron added: "I have had the best head teachers of state schools into No 10.
"I have had the private schools into No 10. I have had the universities into No 10 to talk about university technical colleges.
"The truth is the problem has been not enough good school places in our country... so anyone who can play a role in that - private schools included - is welcome through my door to talk about how we drive up standards."
Eton head teacher Tony Little said he is examining "several possible routes" of increasing links and "ruled nothing out".
Other private schools have already made the crossover, including Wellington College, which set up the state-funded Wellington Academy in 2009.
