Morata only joined Chelsea from Madrid last year, but the Spaniard struggled during his debut campaign in England, scoring just 15 goals in 48 appearances across all competitions and losing his place in the side to Olivier Giroud towards the end of the season.
Speculation has suggested that Morata could leave Stamford Bridge as a result of those troubles, with new manager Maurizio Sarri thought to be eyeing a move for either Robert Lewandowski or Gonzalo Higuain.
Reports in Italy linked Morata with a switch to the Serie A, but Spanish publication OK Diario claims that Morata's father has been in talks with Madrid over a potential return to the Bernabeu.
Madrid are in the market for new forward options following the sale of Cristiano Ronaldo to Juventus, although they would reportedly be unwilling to pay anywhere near the £60m Chelsea spent on Morata last summer.
The 25-year-old still has four years remaining on his contract at Stamford Bridge, but Chelsea may be forced to cut their losses if they are to offload the Spain international.
It is unclear whether new Madrid boss Julen Lopetegui would be open to the idea of signing Morata, though, having left the striker out of his World Cup squad during his time in charge of Spain.