Manchester United are set to increase their offer for Álvaro Morata to £60m after their first bid of around £52m was rejected by Real Madrid.

José Mourinho has identified the 24-year-old as his primary attacking target for this summer after France international Antoine Griezmann confirmed he will not be leaving Atlético Madrid. Negotiations with Madrid have taken place this week, with United’s first offer of €60m (£52.3m) turned down as the Champions League winners value him significantly higher at €90m.

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United are understood to be confident of persuading the Real president, Florentino Pérez, to settle for a reduced fee if they can pay the majority of it up front for a player who returned to the Santiago Bernabéu Stadium from Juventus last year after Madrid exercised a buyback clause of £30m. Chelsea had also registered an interest in Morata, who scored 20 goals in all competitions last season and helped Spain draw their friendly 2-2 with Colombia on Wednesday night, but are now believed to be closing in on a deal for Everton’s Romelu Lukaku.

“Alvaro is a player who wants to play a more important role,” his agent Juanma Lopez told Foot Mercato on Thursday. “He wants to play more. Which is normal for an attacker who has scored 19 goals. I do not know (if he will have another season at Madrid). This has been a brilliant season for Real Madrid who have won many titles. The player will take a clear and definitive decision in the coming days. I have not yet met with the representatives from Real Madrid.”

Asked about reported interest from Milan, he added: “It existed and continues to exist, like other big teams who are interested in a player of his quality.”

Madrid are also keen to sell James Rodríguez, with the Colombia forward thought to be available for around £60m, although there is less enthusiasm for that pursuit at Old Trafford. Meanwhile, Paulo Dybala’s agent has denied reports that the Juventus forward is a target for both United and Chelsea by insisting the Argentina international wants to remain with the Serie A champions. “Paulo signed a new contract with Juventus last month. He is happy in Turin,” Pierpaolo Triulzi told the Guardian.