But former Barca star Bojan suspects Martinez does not have the qualities that Barca require, given their shape and playing style.
And he has warned signing another out-and-out striker could prove an error, after the difficulty Antoine Griezmann has encountered in settling following his move from Atletico Madrid.
With Luis Suarez established as Barcelona's main target man, when fit, Griezmann has been forced into a wide role.
Writing on Spanish website Sport, Bojan said Martinez was well suited to Inter's counter-attacking game, and stressed he was an "excellent" player.
But he also expressed doubt over the Barcelona link, saying: "Inter don't usually take the initiative and that makes me think that Lautaro could occupy an area at Barca that is naturally not his. [That is] something that would certainly be a shame.
"If you allow me a name, I would bet more on Firmino: a link player, with a lot of presence and great mobility. I do not intend that this reflection be interpreted as a refusal to sign the Argentine, but I understand that his profile must be analysed very well because it would be unforgivable that, as happened with Griezmann, we sign a striker to put him on the wing and then complain that it doesn't work.
"That cannot happen again because, although it seems obvious, a nine is a nine. That is his natural habitat and to move him from there is to waste his talent. If Barca need a nine, sign him, but do it to really use him."
Brazil international Firmino joined Liverpool from Hoffenheim in 2015 and signed a long-term contract extension in April 2018, going on to help Jurgen Klopp's team win the Champions League last season and top the Premier League this term.