Morata was signed from Juventus by Chelsea in a club-record deal after Costa, who did not report to training while living in Brazil, was shunned by manager Antonio Conte.
The striker recently secured a return to Atletico Madrid but will not be registered at the Spanish club until their transfer ban expires in January.
"People remember [Costa at Chelsea]," Morata told AS. "I speak to him quite a lot. There was a chance that we might have played together but in the end that didn't happen.
Former Real Madrid man Morata also spoke of the Blues' start to the season, in which the forward has scored eight times in 13 games.
"We've started [the season] well but not everything has gone as we would have liked. We've slipped up in a couple of games and we can't afford to do that.
Morata also netted during the break as Spain defeated Costa Rica 5-0.