He is thought to think the Royal couple are now “shot” of him after a series of scandals involving him and the media.
Before the wedding, Mr Markle staged photographs for the press, and then last month, he broke Royal protocol by revealing Prince Harry’s views on Brexit during an interview with Good Morning Britain.
An inside source told the Mirror: “Thomas is heartbroken.
“He is at a complete loss as to why he has been excluded.”
He is believed to have told pals that Harry and Meghan don’t want anything to do with him any more.
Mr Markle has allegedly said: “I haven’t talked to Meghan and Harry for a long time.
“I think they’re shot of me now.”
The Duke and Duchess of Sussex did not visit Mr Markle when he was in hospital in the days before their wedding.
He had emergency heart surgery which meant he couldn’t travel to the UK for the May 19 ceremony, but thinks his chance to see the Royal couple has perhaps passed.
He has told pals: “I don’t know if she’ll visit.
“I told her not to come and visit when I was in hospital.
“I think that relationship is lost now.”
The Californian found himself at the centre of another Royal scandal this week, when he was outraged the Queen would meet US president Donald Trump before she would meet him.
He said: “If the Queen is willing to meet our arrogant, ignorant and insensitive President she has no excuse not to meet me.
“I’m nowhere near as bad.”
The Queen is due to meet Trump during his visit to the UK next week.
She is expected to host him at Windsor Castle.