Pep Guardiola's side were cleared to compete in next season's Champions League after a successful appeal to the Court of Arbitration for Sport, with the decision also enabling them to press ahead with their summer transfer plans.
City are expected to undergo a significant squad overhaul after surrendering their Premier League title to Liverpool this season, while key players such as David Silva, Sergio Aguero and Fernandinho are coming towards the end of their careers at the Etihad Stadium.
The Daily Mail reports that Martinez could form a part of that overhaul as a long-term replacement for fellow Argentina international Aguero.
Barca are understood to be struggling to meet Inter's asking price, with the Serie A giants unwilling to consider anything less than his £98.8m release clause and attempts to strike a player-plus-cash deal so far proving unsuccessful.
Martinez has scored 18 goals and created six more in 39 appearances across all competitions this season. body check tags ::