The Oliver! star, who is godfather to Paris as well as Jackson’s other children Prince Michael and Blanket, would be willing to take a paternity test, reports the Daily Mail.
He explained: "In 1996 Michael asked me if I would give him my sperm and I said yes. It was a gift to him, no money was paid, it was something I was honoured to do. He wanted children so badly.
"I do feel a definite bonding with Paris and I think there's a definite possibility that she's part of me.
"I want to have contact with her, Prince and Blanket regardless of whether any or all of them are mine. I think it's cruel that I've now been excluded from them."
Lester also noted the similarity between Paris and his daughter Harriet. "Paris is very pale, with blue eyes. All my daughters, apart from my eldest, are fair with blue eyes. So many people have commented on how alike Harriet and Paris look."
The sperm donation was reportedly carried out at a clinic in Harley Street, London in 1996. Paris was born in April 1998.