United fully expect Lukaku to leave the club this summer, which would leave them with just Marcus Rashford and 17-year-old Mason Greenwood as their strikers.
They are eager to recruit a new striker in preparation for Lukaku's departure, and 90min has learned they have been offered both Costa and Higuain on loan this summer, although deals for either are far from certain.
With Higuain - who has been told he can leave Juventus - United have been offered the chance to land him on loan as well, although it remains to be seen if the player would want to return to England, having struggled in his time with Chelsea last season.
The 31-year-old managed five goals in 18 appearances for the Blues, often facing criticism from fans for his disappointing performances. As a result, he may reject the opportunity to return to England.
Last season, Lukaku managed 15 goals in 45 appearances for the Red Devils. He was a vital part of Ole Gunnar Solskjaer's side during the early stages of his reign, but soon found himself struggling to displace Rashford in the lineup.
He has pushed for a switch to Inter, although the Serie A side are yet to submit an offer which would tempt United to part ways with the Belgian.