His performances at Sheffield United have sparked interest from Chelsea who are willing to pay big bucks for the 23-year-old.
But United and Henderson are in talks about a lucrative five-year contract that will make him one of the highest-paid shooters in Europe, Sky Sports reports.
Ed Woodward is set to discuss budgets at Old Trafford with some of the club’s chiefs this week.
United see Henderson as a future No.1, but only signed a new long-term deal with David de Gea last summer.
That leaves Ole Gunnar Solskjaer with a huge decision to make, but the Norwegian has steadily backed his first-choice keeper amid his recent spate of mistakes.
But the Red Devils boss is not opposed to bringing the Englishman back into the fold and allowing him and De Gea to fight for a starting place.
Henderson has kept 13 clean sheets this season at Bramall Lane, which has put him in the running to be England’s No.1 at next summer’s European Championships.
Chelsea boss Frank Lampard will likely be on the hunt for a new goalkeeper after dropping Kepa Arrizabalaga for his final win over Wolves.
The Blues are ready to offer a lot of money and have already shown that they do not wait this summer after adding Hakim Ziyech and Timo Werner.
He supported Solskjaer in a corner and his former teammate turned Sky Sports expert Gary Neville urged him to be ruthless.
He said: “In the last 18 months he has been riddled with errors and only Solskjaer can make that decision on the goalkeeper.
“What I would say about this decision is that Solskjaer has to be decisive and ruthless with this decision, he has to think about himself and the club. If he thinks De Gea is going to return to where he was before, stick with him. “