Morata was bought from Juventus in 2017 for a club-record £60million after Antonio Conte jettisoned Diego Costa.
Despite a dearth of elite-level game time given his talent, the acquisition was seen as a risk worth taking.
The Spanish forward hit the ground running, scoring six goals in his first six league appearances.
But five strikes in his next 25 reflects the season of frustration which typified Morata’s baptism of fire into English football.
This campaign, a respectable record of five league goals in 14 appearances has been blighted by a catalogue of missed chances and the realisation that Olivier Giroud offers a more balanced spearhead to Maurizio Sarri’s formation.
Carragher faced some of the world’s toughest strikers in his 17-year top-flight career, and believes that Chelsea best start seeking a replacement for their lucrative risk.
“As things stand, I find it hard to believe he has a future there,” Carragher wrote on The Telegraph about Morata.
“The notion that a player coming from outside the Premier League needs one season to settle in has always felt wrong to me – the best hit the ground running.
“Morata scored 15 last season as Chelsea’s then new record signing, one fewer goal across all competitions than Drogba did in his first season, but Morata has made much less impact.”
Despite standing at 6ft 2in, Morata does not have the pugnacious streak in him, which epitomised past title-winning Chelsea strikers Drogba and Costa.
“I can see he has great ability but he also strikes me as an opponent whom a good defender can dominate,” Carragher added.
“You can sense his belief slipping with every lost confrontation, and when he starts hitting the deck in challenges well away from the penalty area, then you really know his appetite is slipping.
“The reality is I do not think that Morata will ever click at Chelsea, and I am sure the club think that too. They have to be looking now for a new option next season.”
If there was ever a time for Morata to prove his worth, it is against table-toppers Manchester City on Saturday evening, who are guests at Stamford Bridge.
“Sarri has a big decision to make this Saturday,” Carragher claimed.
“At Napoli last season he had a regular source of goals in his little striker Dries Mertens who got 18 in the league and perhaps Hazard, with seven already, will fulfil that role this season.
“But with every game Morata is giving his club more certainty that this is a signing that has not worked.”