The European champions would look to offer both Morata and Keylor Navas to United in exchange for David de Gea, while Chelsea goalkeeper Thibaut Courtois could be part of the demands in a deal with the Premier League champions.
There had been reports that Morata to United was agreed up on in principle, and the player himself dropped major hints on social media that he was leaving Los Blancos. But the Blues have made a late move for the player.
The Mirror have reported that Chelsea are searching for a replacement for Diego Costa, who is on the verge of a return to Atletico Madrid.
But the potential arrival of Ronaldo would undermine that message, and could give Morata cause to reconsider his options this summer.
Chelsea have also been heavily linked with a move for Everton's Romelu Lukaku, while Conte reportedly told Costa that he is not in his planning for next season.
"I knew they'd bring me back but I didn't know if it was to keep me or sell me".
-It's well known that Ronaldo wants out of Real Madrid, and United are one of the few destinations with the money and power to sign him.
Their need is even more pressing after Zlatan Ibrahimovic's departure, with the 35-year-old having netted 17 of those goals. 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. I'm sure sooner or later I will'.