Palace boss Roy Hodgson has been desperate to sign a new goalkeeper after Vicente Guaita told the club he wanted to leave.
And talkSPORT understands that discussions held are with regards to a loan move with the option to make the deal permanent.
The 26-year-old spent last season on loan at Nottingham Forest and helped them stay in the Premier League.
A permanent move to the City Ground had been expected but a deal could not be struck with United.
Instead, Forest signed Arsenal back-up goalkeeper Matt Turner, leaving Henderson in limbo.
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His future looked destined away from Old Trafford after Erik ten Hag was reunited with Andre Onana, who he coached at Ajax.
Henderson has been desperate for first-team football, which is not possible at the moment at United, his boyhood club.
The England international came up through the academy at Old Trafford and had made it his mission to become the club's No. 1.
But with that out of the window, Premier League clubs have been keen on snapping him up.
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The search for a new goalkeeper has intensified in recent weeks after Guaita told Hodgson that he didn't want to play for the club and would prefer to move back to Spain.
"He [Sam Johnstone] is the only choice at the moment because Guaita is disenchanted with the club and has said he would like to move on," Hodgson said earlier this month.
"He's refused to play in our games so far.
"A complication is that he has a year's contract. It's up to the club to decide, not him. He's made it clear to everybody he doesn't want to be here and compete with Sam Johnstone.
"So Sam Johnstone is No 1 and Remi Matthews is No 2."