Morata, 26, moved to Chelsea from Real Madrid for £60 million in July 2017 but has endured an indifferent spell in the capital city.
He started his Blues career in impressive style as he netted six goals in his first six Premier League appearances.
However, since September last year he has added just 10 more goals in 39 appearances and has often been ridiculed for his gilt-edged missed chances.
Reports in Spanish press claim the former Real Madrid striker 'offered' his services to the LaLiga champions and Alba has since commented on the rumours.
"Morata is a player that I appreciate a lot," he told Goal. "He has been a top player for many years.
"At the end, it's the club's [decision] if they want to sign him or not, as with any other player.
"If the rumours are true, he would be very welcome, as all the new players [are]."