Express Sport understands Antonio Conte is pursuing a deal and will let Diego Costa leave once a move is completed.
The Italian boss knows Morata, 24, well from their time together at Juventus.
And with his game time under Zinedine Zidane limited, a move appears to be in the offing.
Alvaro Morata has been behind Karim Benzema in the pecking order at Real Madrid
The £50million-rated frontman is desperate to leave now more than ever
According to Spanish outlet Diario Gol, Morata has wanted a switch to Chelsea for weeks and has a verbal agreement with the club.
It is said the £50million-rated frontman is desperate to leave now more than ever.
The Spain international has become hugely frustrated with being overlooked repeatedly by Zidane in favour of Karim Benzema.
Madrid’s hitman has endured a difficult campaign, but Morata has still had to remain patient to earn opportunities.
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Antonio Conte wants to reunite with Alvaro Morata at Chelsea
After Madrid’s Champions League quarter-final first leg triumph at Bayern Munich last week, Benzema admitted he had lost five kilos which had helped his performance.
But that only angered Morata more apparently, as it revealed Benzema was playing even all was not well.
It is felt Zidane put him the Frenchman ahead of the team’s needs, and a switch to Chelsea is now Morata’s burning desire.