The Spanish global scored a whopping 20 goals and 6 assists in 43 appearances in all competitions combined, the highest by any Real Madrid player apart from Cristiano Ronaldo, despite largely playing second fiddle to Karim Benzema.
Starsport understands Real Madrid striker Alvaro Morata and Torino's Andrea Belotti are also on the Special One's wish list.
United have recently become the main protagonists in Cristiano Ronaldo's latest transfer saga, with the Portuguese winger thought to favour a return to Old Trafford over any other move.
How did Morata compare to Costa this season?
As a result, the Morata link makes sense, but it will leave United and Mourinho far from impressed if they miss out on two of their top targets to their Premier League rivals.
Recent reports have claimed that Manchester United will officially announce the signing of the Spaniard on Tuesday or Wednesday. However, with no affirmative updates from either side, Chelsea are now looking to hijack United's move.
Chelsea are expecting to lose Diego Costa after boss Antonio Conte texted the striker to tell him he is no longer in his plans.
He is the real deal, and there is still much more to come.
Where could Alvaro Morata go next?
That delay has allowed Chelsea to barge in at the last minute, and the Mirror say Morata's desire to work under Conte could swing the deal in their favour.
The 32-year-old Seleccao star helped Madrid win the La Liga title and was once again fantastic in the Champions League as the Spanish club retained their crown.