Palmer was discussing the impact of Wrexham's star-studded ownership against that of musician Sheeran, who has a vested interest in boyhood club Ipswich.
Wrexham secured promotion back to the Football League last month with a record haul of 111 points.
The club's players and staff were later whisked off to an all-expenses-paid trip to Las Vegas courtesy of Reynolds and McElhenney, to celebrate the fantastic feat.
Palmer spoke about the impact of Wrexham's high-profile ownership on an episode of teammate Ben Foster's Fozcast podcast and drew comparisons with Sheeran and the newly-promoted Championship side.
"There's names as big as [Reynolds and McElhenney] that own football clubs, lower league," said Palmer.
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"Ed Sheeran, Ipswich. I don't know what his share of it is, he's part-owner. Has he done what these two guys have done?"
"Nowhere near it," Wrexham teammate Ben Foster responded. "They have just been promoted, in fairness to them, but still."
Palmer then added: "How long has Ed Sheeran been there? Six years? Seven years? And he's as big as Ryan and Rob, right? Ed Sheeran is huge."
Foster later claimed Sheeran was not in the same bracket as Reynolds and McElhenney before Palmer replied: "I'm putting Ed Sheeran up there. I'll ask you: has Ed Sheeran done as much for Ipswich as Rob and Ryan have done?
"It's not easy what they're doing. They make it look easy. And I'm sure Ed Sheeran's a great guy, I'm just trying to leverage what Rob and Ryan have done - it's not just the status, it's the hard work they've put in."
But their claims have sparked backlash from Ipswich fans who quite rightly pointed out that Sheeran is a sponsor on the club's kit and not the owner.
One fan wrote: "Ed Sheeran's a fan, and has been a shirt sponsor, not quite the same as owning the club lads."
Another added: "Ed Sheeran is just a shirt sponsor, how can you compare them?"
A third user wrote: "Ed's a shirt sponsor, not our owner. He's obviously made a bigger impact than expected as a shirt sponsor for the last few seasons, not an owner for the past six/seven years!! Equivalent to TikTok for you guys. Pleased with what Rob and Ryan are doing with you but guys you've got to correct it."
Meanwhile, Ipswich defender Luke Woolfenden took to Twitter after learning of Foster and Palmer's comments, adding: "What a weird thing to make up".
Wrexham fans will be eagerly awaiting the release of the 2023/24 League Two fixture list when they will be made available on June 22.
The Reg Dragons are preparing for their first season in the Football League since they were relegated to the National League 15 years ago.