The Spanish giants have long regarded the 22-year-old as their number one transfer target this summer, having identified him as an ideal long-term successor for Luis Suarez.
However, Inter's refusal to consider bids of anything below Martinez's £98.8m release clause prevented a deal from being struck, while the Italian outfit can now charge what they want after that clause expired.
Barcelona president Josep Maria Bartomeu this week confirmed that talks over a deal for the Argentine have stalled, but Mundo Deportivo claims that reported interest from Man City has forced the Catalan club to revive their efforts.
Barca have reportedly drawn up three possible deals to take to Inter, one of which would see the Milan club given their choice of Arturo Vidal, Ivan Rakitic or Samuel Umtiti to include in a swap deal.
Option two would see Barcelona sell Ousmane Dembele in order to raise funds for Martinez, while the third option would be to offer Inter £37m plus Junior Firpo in return for the Argentina international.
Martinez has scored 18 goals and created six more in 39 appearances across all competitions this season.