News of a near £30million offer for the highly-rated 23-year-old comes a day after it was revealed the club lost £197million last season, the biggest single-year loss by a football club in history.
But despite the shortfall off the pitch, owner Sheikh Mansour bin Zayed Al Nahyan has no intention of letting up in his quest to conquer Europe on it after his side's Premier League success last season.
And Martinez, who has been watched extensively by City scouts this season with first-team coach David Platt also making a personal check on the player last month, is seen as an integral addition to the side.
The Spain international has enjoyed an impressive campaign in a central defensive role for Bilbao having been converted from his usual holding midfield role by boss Marcelo Bielsa.
His commanding displays at the back have not gone unnoticed with Barcelona also keen on signing Martinez as they look for a long-term successor to captain Carles Puyol.
But they know they know they are unable to match the riches on offer at the Etihad Stadium with City set to test Bilbao's resolve to keep hold of their star man with an offer after the Basque side's Copa Del Rey final clash against Barca on Friday, according to reports.
City's move for Martinez comes as they await a decision over the future of No1 target Eden Hazard who admitted yesterday that he has agreed terms with City, Manchester United and Chelsea.
That decision is expected in the next 10 days with some claiming that the brilliant Belgian winger is leaning towards linking up with compatriots Thibaut Courtois, Kevin de Bruyne and Romelu Lukaku at Stamford Bridge.