Atletico could now sign Morata as Costa's replacement, with the Spaniard struggling to find the back of the net at the Wanda Metropolitano.
"Diego Costa would absolutely transform Chelsea's fortunes and, if it was down to me, I'd break the bank to re-sign him", Crouch wrote of the Spanish striker, who is now sidelined following foot surgery.
Morata's agent is in in London to secure his departure from Chelsea, with a loan until the end of the season and an obligation to buy in the summer the most likely outcome.
However, Atletico manager Diego Simeone remained coy on the interest in Morata.
"The only thing I'm thinking about is the upcoming match against Levante", Simeone told reporters.
"I can't confirm or deny anything because coaches wait to see what the club can do".
'Some players want more minutes, some could be sold by the club, some could arrive. "We need to wait until January 31", he is quoted as saying by the Daily Mail.
On one side you have a striker who did perform for Chelsea, but his issues off the field left his position at the club untenable, while on the other there's Morata, who has been a real disappointment considering the money we paid for him.
Sevilla are also keen on the Spain worldwide, but their sporting director Joaquin Caparros admitted on Tuesday: 'It is true that we have an interest in this player [Morata], but it is a very, very complicated operation.
His former club aren't believed to be interested in signing the Spaniard, with their focus on fellow Chelsea ace Eden Hazard.