The 32-year-old French international is entering the final six months of his contract at the Camp Nou, and as talks over a new deal with the reigning La Liga and European champions stall, Abidal has attracted widespread interest from a host of major clubs.
Barclays Premier League interest is thought to be high, with both Arsenal and Liverpool having been credited with an interest in the former Lyon full-back's services, so the Citizens will face competition for his signature.
Over 40 per cent of the 5,000 votes cast called for Mancini to strengthen City's defensive department with the addition of Abidal, in favour of attacking reinforcements in the form of Daniele De Rossi, Eden Hazard or Edinson Cavani.
Such is the array of attacking talent at the Etihad Stadium, that fans have called for an astute signing to increase Mancini's options at the back, particularly in their time of need with Kolo Toure away on African Cup of Nations duty, and club captain Vincent Kompany currently serving a four-game suspension after his sending off against Manchester United in the FA Cup last weekend.
The Italian tactician surprised many this week when he bemoaned Manchester City's lack of squad depth, calling for further investment in his already star-studded line-up.
"All the people think we have a lot of players. But we have 19, plus keepers," said Mancini. "It is not a big squad.
"If we are unlucky and we have three or four players injured, like at this moment, we can have a problem. The club knows this."
After spending around £250million on new players since his arrival two years ago, and with UEFA's Financial Fair Play regulations just around the corner, Mancini may have to sell before he can bring anyone else in.
With that in mind, a modest move for Abidal who would command a fee in the region of £4million is perhaps the best option for City if they are to conduct any business this month.
The fans seem to recognise the importance of balancing the books, and with no movement on the proposed departures of Nedum Onuoha and Wayne Bridge, the club could still improve their squad with the signing of an experienced international who has been capped over 60 times for his country, and boasts a wealth of domestic and European success.