The France international has long been a target of City, with the club's interest dating as far back as Roberto Mancini’s reign as manager.
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However, Pellegrini has continued to keep tabs on the defender’s progress, sending scouts to watch him alongside teammate Nicolas Otamendi in Porto’s 2-0 defeat against Benfica earlier this month.
The Chilean has given the green light to City launching an ambitious big-money move for the player this week after being given encouragement that Porto could be willing to sell.
Much, though, could hang on Otamendi’s future, with Porto thought to be more keen to allow the Argentine to depart before Mangala, for whom the Portuguese club hopes to encourage a bidding war in the summer with Chelsea and Manchester United having also shown interest.
Still, City is hopeful a the offer – though short of Porto’s asking price – could force through a move that would provide a huge lift to Manchester City as the club prepares for a tough second half of the season.
Pellegrini’s men currently sit second in the Premier League table, two points behind Arsenal with a game in hand and a point above Jose Mourinho’s Chelsea – and the manager is convinced that strengthening his defense could be key as the club looks to regain the title.