Andoni Zubizarreta, the sporting director, is reportedly in Buenos Aires on Monday for talks with Martino, who led Newell's Old Boys to the Argentinian Clausura title last season but recently severed ties with the club.
And Messi, the four-time Ballon d'Or winner, would appear to support such an appointment.
"I like Tata Martino," he told Diario Ole. "He is a great coach and he showed that in the Clausura with what he did for the team, the way it ended and how he did it. He gets his teams playing well and we all respect him."
The Catalan club announced on Friday night that 44-year-old Vilanova was stepping down as he continues his battle with cancer.
Martino, the Former Paraguay coach, has been heavily tipped to take over ahead of the likes of Andre Villas-Boas, Michael Laudrup, Marcelo Bielsa, Luis Enrique and Rubi.
Ronald Koeman, the Feyenoord coach, ruled himself out of contention to succeed Vilanova after Sunday's pre-season friendly draw against Dordrecht.
Quoted in the Dutch media, the former Barca and Holland defender said: "That is absolutely not on the cards for me.
"I do not know who it should be. It's not something that affects me now. I'm more worried about the disease Vilanova has."
Sandro Rosell, the Barca president, said on Friday night that the club expect to make an announcement on Vilanova's replacement in the coming days.
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