De Gea was given the nod between the sticks for the Europa League final, but the Spain international conceded all 11 of Villarreal's penalties in the shootout before missing his own effort to hand the La Liga side the trophy.
The 30-year-old had lost his spot to Henderson in the latter stages of the season but was handed starts in the league against Leicester City and Fulham before being given the nod in the European final.
However, according to The Mirror, Henderson will be given the gloves at the start of next season, with De Gea potentially leaving the club in the upcoming market.
Henderson's own future at Old Trafford has also been called into question, as the 24-year-old has also had some difficult matches during the 2020-21 campaign.
The England international ultimately finished the season with 26 appearances, 13 of which were in the Premier League, while De Gea made 36 outings in all competitions during the recent campaign.