Bruno Fernandes, Marcus Rashford, Harry Maguire and Luke Shaw are all on Solskjaer's list for new deals, while it is hoped Paul Pogba can be persuaded to extend his contract, which is set to expire next summer.
Fernandes still has five years left on his contract, but Solskjaer is keen to bring his £100,000-a-week deal in line with the club's top earners.
Maguire's contract has four years to run, while Shaw and Rashford's deals each end in two years.
All three players, who earn between £180,000 and £200,000 per week, will be offered terms similar to Fernandes.
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