United had been favourites to sign Real Madrid wantaway Morata - with a £65m deal appearing close to completion last week - but the Blues have barged in.
But Chelsea's interest will be of concern to Mourinho - particularly given the player's affection for Conte - the manager who signed him for Juventus in 2016 before taking over the Italian national team.
Morata has stated in the past: “Conte is the manager who most 'bet' on me, without even ever having had me in his team. I'm very conscious of that: he bet on me for Juventus but left before I arrived; then he wanted me at Chelsea come what may. He knows me better than I could imagine, I'm sure, and that's important: it motivates you to work hard, train well.
“I feel indebted to him because he's the coach that most trusted in me, most wanted me, who made me feel I could perform at the highest level. And yet I've never had the fortune to actually work with him. I'm sure sooner or later I will."