The Real Madrid striker has emerged as Mourinho’s top target to replace Zlatan Ibrahimovic after Chelsea edged ahead in the chase for Everton star Romelu Lukaku.
According to Spanish paper Marca, the United manager has been in touch with Morata on two seperate occasions in a bid to convince him about moving to Old Trafford this summer.
It’s claimed Mourinho told him: ”Come to me, you will be important.”
Morata looks set to leave the Bernabeu after enduring a frustrating campaign last term.
Despite hitting 20 goals in all competitions, manager Zinedine Zidane restricted him to just 19 starts.
Starsport understand Morata has told Real Madrid chiefs he wants out.
Morata’s agent Juanma Lopez recently admitted the Spain international’s frustration at his lack of action.
"He does not want a season like this again,” Lopez said. “It was a great season, but he wants to play more.
"The player will take a clear and definitive decision in the coming days. I have not yet met with the representatives from Real Madrid.
"Alvaro is a player who wants to play a more important role. He wants to play more.”
According to Marca, Lopez is set to meet with Bernabeu chiefs tomorrow.
United are expected to launch an offer at the same time.
Real Madrid hope it will be in the region of £79m (€90m) but it is more likely to be worth £61.5m (€70m).
Meanwhile, Spanish website Diario Gol claim a deal could be reached between the two clubs in the next 48 hours.
Yesterday, United announced they had reached an agreement with Benfica for Sweden defender Victor Lindelof.
They will pay the Portuguese side £35m for the centre-back, who will undergo a medical after the international break.
