Reports in the Spanish media claim Martino, who most recently was head coach of Argentine Primera Division outfit Newell's Old Boys before stepping down earlier this month, has signed a three-year deal to replace Tito Vilanova.
Barca star Lionel Messi, who played youth football for Newell's, has already backed Martino as a prime candidate to take over at the Catalan club, and the 50-year-old Argentine coach is seen to be the perfect option to continue the side's football philosophy.
"I like 'Tata' Martino," Messi told Diario Ole.
"He is a great coach and he showed that...with what he did for (Newell's), the way it ended and how he did it.
"He gets his teams playing well and we all respect him."
With Vilanova having stepped down as Barcelona coach on Friday due to his continuing treatment for cancer, the Catalan club made it clear they wanted to find a replacement quickly and Martino's availability has taken him to the top of the list.
Barcelona were also reportedly interested in Luis Enrique and Ernesto Valverde but that duo have recently signed with Celta Vigo and Athletic Bilbao respectively, ruling them out of contention.
Martino, who stepped down as Newell's boss after they were eliminated in the semi-finals of the Copa Libertadores on July 10, led the Rosario-based club to the Torneo Final championship, as the second half of the Argentine football season is called, in June.
The Rosario-born coach is considered a disciple of highly-rated Argentine tactician Marcelo Bielsa, who most recently coached Athletic Bilbao, and Martino has praised Barcelona's possession-based attacking style of play.comments