The 26-year-old has been given the green light to make his departure from Old Trafford this summer after failing in his attempts to become the Red Devils' number one.
Following public criticism of his treatment last summer, Henderson was loaned out to Nottingham Forest and kept six clean sheets in 20 games to help the Tricky Trees stay afloat in the Premier League.
Fellow loan signing Keylor Navas stepped in while Henderson was recovering from injury, but Steve Cooper's side were still believed to be interested in a permanent deal for the England international.
However, having failed to reach a compromise with Man United, Forest brought in Matt Turner from Arsenal instead, and Palace are now considered the frontrunners for Henderson's signature.
The two clubs have apparently been in talks over a loan-to-buy deal, but according to the Daily Mail, the two clubs remain locked in negotiations over the fee.
The Eagles are expected to wave goodbye to Vicente Guaita before the end of the transfer window, as the Spaniard has lost his spot in goal to Sam Johnstone and let his frustrations known on social media.
Replying to a tweet from the official Palace account on the opening day of the season against Sheffield United, where his name was not included on the team sheet, Guaita said: "Where is my name? So how can I play for Palace?"
With Guaita frozen out, Johnstone kept a clean sheet against Sheffield United before giving away Arsenal's game-winning penalty on Monday night, bringing down Eddie Nketiah in the box.
Henderson's possible arrival at Selhurst Park would see the Englishman end a 12-year stint at Old Trafford, where he has been loaned out to five different teams in Forest, Sheffield United, Stockport County, Grimsby Town and Shrewsbury Town.
Since his belated first-team emergence, Henderson has recorded 13 clean sheets from 29 matches for the Red Devils and ousted David de Gea from the XI for a short period of time in 2020-21.
However, De Gea quickly won back his place in the team, and following the Spaniard's exit, Andre Onana has been instilled as Erik ten Hag's undisputed number one.
Ahead of Henderson's expected exit, Man United have supposedly conducted medical tests on Fenerbahce's Altay Bayindir, who could join the Red Devils for just €5m (£4.3m) if scans on a back injury provide reassuring results.
A move for unsettled Benfica goalkeeper Odysseas Vlachodimos has also been mooted, as the Greece international was dropped from the Eagles' squad last weekend following a falling-out with manager Roger Schmidt.
Henderson is expected to be on the bench at best when his former loan club Forest head to Old Trafford to face Man United in their next Premier League battle on Saturday afternoon.