Since making the move from Real Madrid in 2017, Morata has scored 16 goals in 45 Premier League matches for the Blues, with six of those strikes coming in his first six league games.
"Morata is a player that I appreciate a lot, he has been a top player for many years," Alba said on Thursday.
"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]."
Morata would likely only be allowed to leave Chelsea in the transfer window upcoming if coach Maurizio Sarri can source a replacement - with Olivier Giroud the only other senior striker in the squad.
Belgian attacker Michy Batshuayi is one player who could fill the void, with his loan club Valencia reportedly keen to send him back to London in January.
Another is loanee Tammy Abraham who has impressed during his short spell at Aston Villa, where he has netted seven in his last five.
While speculation will continue around Morata and his future, any potential transfer dealings could be dealt a blow by the injury the 26-year-old picked up in Thursday’s 2-2 draw with Hungarian side Vidi .
However, initial fears that it could be a long-term issue were partly quelled by Sarri after the game, when he admitted to the press that he does not believe the injury looks serious .