The club only handed an 18-month contract to Tim Sherwood in December following the sacking of Andre Villas-Boas, but are understood to be reviewing his position after a poor run of results.
Sherwood suffered a nightmare week last week, losing 4-0 to Chelsea, 3-1 at home to Benfica and 1-0 at home to Arsenal in the north London derby.
That run of results and public criticism of his team has seemingly put his position under pressure, and the club are monitoring Martino’s position at the Nou Camp.
The Argentine may be forced to quit Barca in the summer, with the Catalan giants currently occupying third place in La Liga, four points behind leaders and bitter rivals Real Madrid.
The 51-year-old is already in talks over his future, with reports suggesting he is already planning for life in the Premier League next season.
Reports suggest the Argentine coach has sent his agent to England to sound out potential Premier League clubs.
And while Louis Van Gaal remains a top managerial target for Tottenham chairman Daniel Levy, but Martino is also understood to be in the running.