The 25-year-old has been a key player for the Three Lions in their run to the quarter-finals of the competition, most notably bagging a fine individual goal in the 6-1 win over Panama.
Lingard has also done a job when called upon by Jose Mourinho at club level, with the former Leicester City and Birmingham City loanee featuring 48 times in all competitions last season.
The Sun claims that United now intend to tie Lingard down to another improved contract to double his current salary, despite only signing a four-year deal worth £75,000 a week in April last year, as they see him as a potential superstar.
An Old Trafford source is quoted by the publication as saying: "Jesse has shown that he is a top class performer on and off the pitch.
"He has a fabulous season for the club last year and has taken that form onto the international stage so far. His England showings has been brilliant and the club know he is all set to become a global star if he continues."
Lingard contributed directly to 13 goals in the Premier League last season - eight of his own and five assists from attacking midfield.