Manchester United are set to make an improved offer of €75m (£65.8m) to Real Madrid for Álvaro Morata as José Mourinho steps up his attempt to replace the departed Zlatan Ibrahimovic for next season.

Negotiations with Real have been in progress for several weeks, with United having seen two offers of €60m (£52.3m) and €70m (£60m) turned down at the start of June as the Champions League winners value him significantly higher at €90m. Having identified the Spain striker as his transfer priority for this window with Wayne Rooney close to agreeing a move to Everton, Mourinho is understood to have grown frustrated over the lack of new arrivals having so far only completed the £30m signing of Victor Lindelof from Benfica.

United are due to fly out for their pre-season tour of America on Sunday and the Portuguese is hopeful that the deal for Morata, who he coached during his spell at the Santiago Bernabéu Stadium, could still be completed in time for him to join up with his new team-mates.

The frosty relationship that exists between them and the reigning European champions has not helped matters, with United insistent that goalkeeper David de Gea will not be leaving Old Trafford this summer. However, with the new offer edging closer to Real’s valuation, it is believed that they could be close to accepting a deal that would see Morata leave the club for the second time in his career, having first moved to Juventus in 2014.

He is already understood to have told Real that he wants to join United and has agreed personal terms on a contract worth around £4m a season. Reports on Wednesday suggested that United have also rekindled their interest in signing Everton’s Romelu Lukaku but is understood that Morata, who scored 20 goals in all competitions last season, remains Mourinho’s preferred option.