The Barcelona star was the subject of scrutiny after he went to a casino in Spain in the build-up to the clash with Manchester City, along with team-mate Gerard Pique and the Chelsea midfielder.
And Messi has again caused something of a stir after a night out in London on Sunday along with former Barca team-mate Fabregas, with whom he remains close friends.
The pair visited 'Colony Club', an exclusive casino in Mayfair, with girlfriends Antonella Roccuzzo and Daniella Semaan.
Messi was linked with a possible sensational transfer to Chelsea earlier this season when tensions with head coach Luis Enrique came close to breaking point.
The 27-year-old fanned the flames of the rumours by following the Blues' official page on Instagram.
While Messi has maintained he is happy with the current Liga leaders, speculation over his future remains rife, with the Argentina international and Luis Enrique still not on full speaking terms at Camp Nou.
Barcelona sporting director Ariedo Braida has admitted that, while Messi's sale remains highly unlikely, a transfer cannot be ruled out due to the player's €250 million release clause.
"I think that it is nearly impossible to see Messi leave Barcelona, but it could happen with clubs like PSG and Manchester City around, who have a lot of money to spend," Braida told Esport 3.
"Strange things happen every now and then."
Messi has been in exceptional form in recent weeks, with his hat-trick in the 6-1 thrashing of Rayo Vallecano drawing him level with Cristiano Ronaldo in the race for the European Golden Shoe.
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