Once again, the England international's future is clouded in uncertainty following the end of his most recent loan spell with Nottingham Forest, where he kept six clean sheets in 20 games.
Henderson's efforts helped keep Steve Cooper's men in the top flight, although Paris Saint-Germain loanee Keylor Navas stood in for him towards the end of the campaign while he recovered from a thigh injury.
Forest have been pursuing a permanent deal for Henderson, but with conversations failing to yield a positive solution, they instead moved for ex-Arsenal shot-stopper Matt Turner.
Tricky Trees head coach Cooper is still believed to be keen on signing Henderson as competition for Turner, but as things stand, a permanent move to the City Ground is unlikely to happen.
However, Henderson could be offered an alternative escape route from Old Trafford, as The Sun claims that Palace are now hoping to bring the 26-year-old to Selhurst Park.
Roy Hodgson's side are expected to wave goodbye to Vicente Guaita before the end of the transfer window, leaving Sam Johnstone short of experienced cover in between the sticks.
Man United are supposedly prepared to let Henderson depart on loan with an obligation to buy in 2024, although the Eagles would find it difficult to sign him on a permanent basis.
Such a stipulation is what is believed to have led to a breakdown in talks with Forest, as Man United insisted on a straight cash sale this summer or an obligatory permanent move if he played enough games for Cooper's side.
Nevertheless, Palace are open to a transfer under the right conditions and are working to find an amicable solution, but Southampton's Alex McCarthy and Leicester City's Daniel Iversen are alternative options.
Henderson has been on the books at the Theatre of Dreams since 2011, but the English shot-stopper has played just 29 matches for the senior Man United team in all tournaments, keeping 13 clean sheets.
The 26-year-old was loaned out to Stockport County, Grimsby Town, Shrewsbury Town and Sheffield United before his first-team breakthrough, helping the Blades earn promotion to the top flight in 2019.
Henderson briefly relegated David de Gea to the bench in the 2020-21 season, but the Spaniard quickly regained the number one spot, and Henderson has not played for the Red Devils since February 2022.
Having recovered from his thigh issue, Henderson has been back on the bench for Man United's opening two Premier League games of the season against Wolverhampton Wanderers and Tottenham Hotspur, playing second fiddle to Andre Onana.
The Red Devils succumbed to a Pape Sarr strike and Lisandro Martinez own goal in a 2-0 loss to the Lilywhites on Saturday and will aim to recover at home to Henderson's former club Forest next weekend.