De Gea's deal at Old Trafford is set to expire on June 30 but talks over a new contract are at an advanced stage.
United expect the Spaniard to extend his stay and once it's confirmed, they are prepared to let Henderson negotiate a move to Forest.
Henderson spent last season on loan at the City Ground and Forest made enquiries throughout the campaign about making the move permanent.
United's agreement with Forest last summer was a straight loan and a full transfer will require further talks between the two clubs.
Henderson has a contract until 2025 with the option of another year and United will ask for a sizable fee before letting the 26-year-old England international leave.
Forest boss Steve Cooper wants Henderson to be his No. 1 next season after Keylor Navas, who joined on loan in January, left the club at the end of the season.
Henderson missed the last four months of the season because of a thigh injury but is hopeful of being fit for the start of preseason.
United, according to sources, may look to sign another goalkeeper this summer.
Manager Erik ten Hag wants De Gea to stay but the 32-year-old's status as the club's first-choice goalkeeper is not guaranteed.