The retired Hollywood lighting director said he would appreciate anything the 92-year-old monarch could do to help him reconnect with the Duchess of Sussex.
The direct appeal came as the estranged father revealed he had been texting Meghan, 37, everyday – but was yet to receive a reply.
Speaking today with Good Morning Britain, the American said: "I would appreciate anything she (the Queen) can do.
"I would think she would want to resolve the family problems.
"All families, royal or otherwise, are the same and they should be together – certainly around the holidays."
The Sussexes will be with the Queen at Sandringham this festive season.
Morning show host Piers suggested the Queen had previously become involved to help in family problems, including in marital problems between Princess Diana and Prince Charles.
He praised her as being a "very humane woman, a very wise woman".
And the outspoken host – who has previously blasted Meghan for "ghosting" friends and family – said he was devastated on behalf of Thomas Markle for not being able to speak to his daughter.
Thomas said he had not even received a Christmas card from the Duke and Duchess of Sussex to celebrate the festive season.
It comes after the Duchess of Sussex was encouraged to go to the Queen for advice amid rumours of a rift between the Fab Four.
A royal insider told the Sunday Times: "Her Majesty has seen it all and could offer the duchess some helpful advice at the moment.
"Meghan would do well to nurture that relationship and pop over for the occasional cup of tea with the Queen.
"That is what Sophie Wessex has quietly done so well."
Prince Charles is also said to have tried to smooth things over with an invite to Anmer Hall – William and Kate’s Norfolk country home – but it backfired and the couples reportedly had a “ghastly row”.
It comes as pregnant Meghan and Prince Harry, 34, revealed they would be leaving the home they currently share with the Cambridges at Kensington Palace.
Overnight, claims also surfaced that the Duke and Duchess of Sussex had been nicknamed Monica and Chandler due to Meghan's controlling behaviour – much like the Friends character.
Thomas Markle attempted to defend his daughter from the claims the former American actress was "demanding", saying she would always remain polite.
But he admitted: "She has always been a very controlling person and that is part of her nature but she has never been rude.
"The ghosting I don't completely understand – she's always been in charge, that's her nature, but not been rude."
Thomas said he was yet to meet Prince Harry, but hoped he would one day be able to reconnect with the couple and meet his future grandchild.
He added: "There has to be a place for me. I'm her father and I will be the grandfather to her child.
"I'm here and she knows it."
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