Henderson spent last season on loan at Nottingham Forest, although he was restricted to just 20 appearances in all competitions due to a thigh problem that ended his campaign in January.
The England international is currently training with Man United at Carrington amid the speculation surrounding his future, with Forest said to be keen to sign him on a permanent basis.
However, there is nothing imminent when it comes to the 26-year-old, so according to the Manchester Evening News, he could travel with the Red Devils to the United States on Wednesday.
The report claims that Forest had proposed another loan deal with an obligation to buy, but Man United are only interested in a permanent sale during the summer market.
Henderson is allegedly expecting to complete a permanent move to the City Ground, with the two clubs likely to find a compromise over the next few weeks.
The Englishman's most productive campaign at Man United came in 2020-21, when he featured on 26 occasions in all competitions, becoming the club's number one ahead of David de Gea.
However, Henderson only featured three times for the Red Devils in 2021-22 and then spent last season on loan at Forest, which proved to be his sixth loan spell away from the club.
There is also uncertainty surrounding Tom Heaton's future, with the experienced goalkeeper left out of the squad for Wednesday's pre-season contest with Lyon in Edinburgh.
Nathan Bishop, Elyh Harrison and Matej Kovar are the three stoppers set to be involved against Lyon, but the club's goalkeeping department will soon be boosted by the arrival of Andre Onana.
The Cameroonian has confirmed that he is joining Man United from Inter Milan this summer, and he is set to undergo a medical with the club on Wednesday ahead of signing a five-year deal.
The Red Devils are said to be looking to sign a second goalkeeper, with Zion Suzuki, who represents Urawa Red Diamonds, believed to be an option.
Man United will take on Arsenal, Wrexham, Real Madrid and Borussia Dortmund during their pre-season tour of the United States before returning to Europe for their final two friendlies of the summer against Lens and Athletic Bilbao.