"Prince Harry and Meghan are top of the pile as David and Victoria are good friends with them and know their attendance would make the day even more special.
"Their schedules are so hectic that David and Victoria want to get their invitations out as quickly as possible."
Reps for the Beckhams would not comment when approached by MailOnline. Harry and Meghan's reps have also been contacted.
Other potential high-profile guests include Sir Elton John, Brooklyn's godfather.
Elton John is also close friends with Harry and Meghan - he performed four songs at the royal wedding.
Former pro footballer David Beckham spoke earlier this year about how "proud" he was of his "amazing" friend Harry following his marriage to Meghan and becoming a father to their son Archie.
He praised Harry for "growing up" and making the decision to step down from his royal role and move to the US.
"I haven't spoken to Harry about him moving," he told ET Online. "We speak as friends and that's the most important thing for me.
"I think he's enjoying being a young father for the first time and that's what we always spoke about.
"We love him and he's an amazing person - and that's the most important thing - but I'm proud to see him growing up as an individual and being that person that every father wants to be," he added.