The Catalan giants have made it known they are keen to strengthen their attacking options and are exploring all options after failing to land Liverpool star Philippe Coutinho.
A long-term injury to new signing Ousmane Dembele has increased the need to draft in at least one new forward, and reports in the Spanish press suggest that Martial is an option for them.
Again the report focuses on the fact that Martial would prefer to play down the middle rather than out wide, and Barca believe he is capable of filling that position for them.
Much is also being made of the Frenchman's failure to start games for the Reds, and it has been suggested he could push for a move if Barcelona pursue an interest.
Reds boss Jose Mourinho is sure to knock back all interest in Martial, who is clearly a key player for the Reds, but that may not stop Barca from making an approach in January.