The midfielder would play alongside Messi for three seasons, winning a league title and the Copa del Rey before joining Chelsea.
Messi could be set to follow his former team-mate through the exit door this season, after his contract expired last week with a new deal yet to be agreed between Barca and the superstar.
The Argentine has become one of the best footballers of all time during his 17-year spell in Barcelona ’s first team.
He has won 10 La Liga titles and four Champions Leagues, as well as six Ballon d’Ors across his senior career at the Nou Camp.
Messi is also Barcelona’s record goalscorer and has set a plethora of records in the Spanish top-flight.
Despite approaching the twilight of his career, Messi has continued to be Barca’s most important player.
He scored 38 goals and notched 17 assists last season, in what was ultimately a disappointing campaign for Ronald Koeman’s side.
But his time with the club could be coming to an end, with Messi currently a free agent having seen his deal expire.
Barca club president Joan Laporta has taken personal control of negotiations with Messi and his representatives.
Despite that though, the two sides remain at a standoff and appear to be no closer to coming to an agreement.
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Messi is currently starring for Argentina at the Copa America, scoring four goals to send his side into the semi-finals.
And with Messi still producing at the top-level, Barca will need a new superstar to become the focus of their team if he does indeed depart.
Fabregas believes that man could be Pedri, who has enjoyed a breakthrough season with Barca, scoring four goals and notching six assists in 52 appearances in all competitions.
The 18-year-old is currently playing for Spain at Euro 2020, starting all of their matches so far as they reached the semi-finals.
And Fabregas has stated his belief that Pedri’s performances at the tournament are showing he can take over from Messi.
“He started a little bit slow, but again like the team, he’s growing into the tournament. He played a fantastic season for Barcelona,” he told talkSPORT.
“I mean, he’s only 18, we cannot forget that. He’s a special talent and I think he’ll be a superstar in the near future.
“But what I like is the confidence that he has got. He’s always asking for the ball. OK, sometimes can be better or other times he can make other decisions.
“But I believe that he is showing always for the ball, he wants the ball, in difficult moments he’s there to be available and this is what I like, his personality.”