Lukaku, 24, recently suggested that remaining a part of Ronald Koeman's side is "not an option" and made his desire to leave Goodison Park very clear earlier this year. The Belgium international's preferred move was Chelsea, who have been pursuing him for over a year, but BBC Sport report that Jose Mourinho's men have made the first move.
Manchester United and Chelsea both submitted bids for Lukaku earlier in the summer, but the Red Devils' interest seemingly grew cold and they instead pursued a deal for Morata, who seemed destined to leave Real Madrid.
But now Manchester United have switched their attention away from Morata and onto former Chelsea prodigy Lukaku, who scored 25 Premier League goals for Everton last season.
Lukaku's move to Old Trafford will all but pave the way for Manchester United captain Wayne Rooney to return to his boyhood club this summer, and it is understood that England's all-time top goalscorer could complete his return to Everton by the end of the week.
Rooney fell down the pecking order at Old Trafford last season and is also of interest to clubs in China and the US. But the 31-year-old's preferred destination has always been Everton, who have splashed out close to £100m already this summer.
Koeman's side have already spent large amounts of money on Michael Keane, Jordan Pickford, Davy Klaassen and Sandro Ramirez, and are still keen on signing Arsenal's Olivier Giroud, Swansea City playmaker Gylfi Sigurdsson and a replacement for Lukaku, the focal point of the Blues for so long.
Morata is now left in limbo. The €90m-rated Spain international was fully expecting to leave Real Madrid for Manchester United this summer. He was reported to be a target for Chelsea earlier in the year, and Antonio Conte's men could reignite their interest after falling behind in the race for Lukaku.