Pep Guardiola's side are willing to activate his £97.4million release clause this summer according to The Sun.
Chelsea as well as La Liga giants Real Madrid and Barcelona are also in the hunt for the striker.
Even so, Inter Milan vice-president Javier Zanetti is confident that Martinez will stay at the club despite interest from Barcelona.
Martinez has been hugely impressive this season - he has scored 16 goals in 31 appearances across all competitions.
However, Zanetti believes that Martinez won't be leaving the Serie A side any time soon.
'Right now we're not talking about the transfer market, the most important thing is health,' Zanetti told ESPN.
'I see him happy at Inter, he's identifying himself with the club. We believed in him. I see his future at Inter.'
Barcelona are looking to bolster their attacking options, and Martinez, at the age of 22, would represent a useful long-term option.
Martinez has already played alongside Lionel Messi for Argentina and could be tempted by the prospect of linking up with his compatriot at club level.
Having started out at Racing Club, Martinez made the switch to Inter 2018 and has proceeded to produce some impressive performances.
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