The Sun says the Polish striker earns £2million a year — almost £40,000 a week — at Borussia Dortmund.
But United would be prepared to pay him £90,000 a week — nearly £4.7m a year.
After being denied a move to Bayern Munich, Lewandowski said: “I do not think that this is the final decision and I expect the situation to change.
“I am enjoying my holiday for now but I hope things move forward pretty soon and the situation changes.
“I do not get upset about anything.”