The goalkeeper has impressed for Chris Wilder's side throughout the 2019-20 campaign, and there has been talk of the 23-year-old potentially challenging David de Gea for the number one spot at Old Trafford.
Henderson has kept 10 clean sheets in the Premier League this season, but he will see his loan deal with the Blades expire in May as the coronavirus pandemic threatens to put the league on hold until the summer.
According to the Evening Standard, Henderson could face a period of uncertainty if England's top flight did not reach a conclusion by June, and there are supposedly no guarantees that football will be resumed by April 30.
The report also claims that Wilder is open to keeping Henderson on the books at Bramall Lane for another year, and there is a suggestion that contracts set to expire this summer could be extended until the end of the season.
Henderson's current deal with the Red Devils will run out at the end of the 2021-22 season.