Mourinho has been linked with a number of other players in recent weeks, however, most prominently Inter Milan winger Ivan Perisic, and The Sun claims that he has been given the green light to push ahead with a fresh bid.
It is suggested that the Portuguese could hand over £35m to finally land Perisic, who has already been the subject of at least one failed bid, although Inter are refusing to offload one of their key players.
An Old Trafford source is quoted as saying: "The club have already invested a lot into the playing squad this summer. But there is still a lot left in the coffers and it's all there for Jose to spend on whoever he likes.
"Lukaku and Lindelof were just the start of what is going to be a busy summer at Old Trafford with lots of ins and outs. This is going to be a huge window for the club with loads of players leaving and plenty coming in as well."
United have also been busy getting unwanted players off their books during the off-season, selling Adnan Januzaj to Real Sociedad for just short of £10m and offloading Wayne Rooney to Everton earlier this week after cutting short his contract.