Williams and Henderson have both signed long-term deals at Old Trafford within the last 12 months, but the club are considering fresh terms to reflect their impressive development.
Williams, 19, was not part of Ole Gunnar Solskjaer's preseason tour squad last summer but has broken into the senior squad this season and made 26 appearances in all competitions.
Henderson has spent the campaign on loan at Sheffield United, where his performances have caught the attention of Chelsea, Borussia Dortmund, Paris Saint-Germain and Juventus, as well as England boss Gareth Southgate.
United are keen to keep Henderson, 23, at Old Trafford in the hope he can succeed David De Gea as No.1 in the future but are wary of rival clubs offering regular first-team football earlier.
Henderson has made 27 Premier League appearances so far this season as Sheffield United have recorded the second-best defensive record in the division behind leaders Liverpool.
Both English academy graduates, Williams and Henderson are central to Solskjaer's long-term vision.
Henderson is set to extend his loan stay at Sheffield United until the end of the season after the Premier League campaign was delayed because of the coronavirus pandemic. The league is set to restart on June 17.
Sheffield United are competing with United for a place in Europe next season but sources have told ESPN that club chiefs believe it would look hypocritical to ask Shanghai Shenhua to extend Odion Ighalo's loan at Old Trafford while refusing to allow Henderson to stay at Bramall Lane.