Sources close to Thomas Markle tell TMZ ... he's not traveling to London -- or making any plans to do so -- despite the fact his daughter is due to give birth to her and Prince Harry's child any day now. Meghan's mom, Doria Ragland, arrived this weekend.

We're told, unlike last year -- when health issues kept Thomas from attending the Royal Wedding and giving Meghan away -- the reason he's not visiting his daughter and meeting his new grandchild is because he's squarely persona non grata.

Our sources say Thomas has been unable to make inroads reconciling with Meghan because he believes she's in a "cone of silence" ... but he hopes their relationship can be repaired after she has a baby.

As you'll recall ... Thomas seemed to get shunned by the Royals shortly after the wedding for going to the media, a move perceived by many as self-serving. There's been a lot of speculation about the father-daughter relationship since then, but it's clear they haven't been on speaking terms since August.

Regardless, we're told Thomas, of course, wishes Meghan and Harry the best and hopes for a safe delivery of a healthy baby ... and he's glad Doria's made the trip to be by her side.