The 43-year-old said on Channel 4's Sunday Brunch that he wrote to the former Suits actress and offered his services free of charge, but failed to hear back.
"I did actually write and say if they want the food sorted I would bring the best of British and American chefs together to do the catering,” Jamie confessed.
"I didn't get a reply. That is a true story."
The chef added he would have “done it for free”.
“You know, I like a bit of a moment. I would have got all the American gang over and got all the British dudes. It would have been the best brigade of kitchen ever," he said.
Fellow guest Emilia Fox called it a "massive missed opportunity”.
"I imagine they have all their chefs at Buckingham Palace doing it," host Tim Lovejoy added.
"They are very slick at protocol and getting those gigs done, so we probably were a bit renegade," Jamie added.
The catering for Meghan and Harry’s wedding ended up being looked after by the Queen’s chef Mark Flanagan and his team of 30 staff.
"We know the couple wanted us to make sure we used all of the local seasonal produce as much as possible throughout their menu, and this recent good weather is really helping us to achieve that.
“We are using produce off Her Majesty's estates and that features very much."
Mark also said that the couple “tasted everything” and were “involved in every detail”.