The 25-year-old left Santiago Bernabeu in pursuit of regular first-team football during the summer of 2017.
A £70 million deal took him to Stamford Bridge and a flurry of seven goals in eight appearances suggested that the Blues had invested wisely.
Morata has, however, added just five efforts to his tally since then and has gone 13 games without finding the target.
Antonio Conte appears to have lost faith in the misfiring frontman, while he has also been omitted from the latest Spain squad.
Carvajal would welcome the frontman back, telling El Transistor when asked if he sees Morata taking in a third spell with the Blancos: “Yes, he’s a good friend and a very good player.”
He is eager to make his mark at Chelsea, with there a determination to play his way into form, but Madrid will always be home.
In an interview with Movistar+ in February, Morata said: “Obviously I have to respect Chelsea, who made a huge effort to sign me and I'm very happy here.
“But Madrid will always be Madrid for me.”