"Even though things are tense between Prince Harry and Charles, one thing they do agree on is it shouldn't affect Archie and Lili's relationship with their grandfather," says the source.
"He's pinning a lot of hopes on seeing Archie and Lili on his birthday. It's his one big wish and he'll be crushed if it doesn't happen."
Despite only meeting Archie, four, and Lili, two, a handful of times, the King adores being a grandpa.
So much so, he has reportedly extended the tots an invite to stay with him at Highgrove, so he can get to know them even better.
He also hopes he and Archie can bond over their joint love of gardening.
"Charles does get to see them on FaceTime every couple of weeks and he's completely besotted," tells the source.
"He's thrilled that Archie has inherited his love of gardening and dreams of showing him around one of his great pride and joys: his gardens at Highgrove."
When Charles purchased Highgrove Estate in 1980, the gardens were completely overgrown.
But thanks to the monarch's green thumb, the gardens are now flourishing and serve as a sustainable habitat for birds and wildlife.
Given Archie's love of feeding the chickens at his Montecito home, the prince will no doubt adore exploring the gardens.
However, his mum Meghan's 'refusal' to step foot in the UK could put a dampener on Charles' plans.
"Unfortunately, the sticking point is their mother's refusal to enter the UK and her refusal to allow their father to take the children there without her," explains the source.
"But Charles is not giving up and he'll always believe his son will eventually do the right thing."