Having signed a three-and-a-half year contract when succeeding Hughes, Mancini had suggested that his position would be reviewed following an initial six-month period at the end of the season.
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Under Mancini, City have won six of their last eight games, with only an injury-time goal by Wayne Rooney during Wednesday's Carling Cup semi-final against Manchester United ending hopes of the club's first major cup final since 1981.
But although the team's resurgence under Mancini has been noted by chairman Khaldoon al-Mubarak and Cook, the return to prominence of players who had been overlooked by Hughes, such as Martin Petrov, Javier Garrido and Micah Richards has been viewed as a more impressive feature of the manager's influence.
Mancini, who continues to pursue Middlesbrough winger Adam Johnson, will receive comprehensive backing in the transfer market in the summer, although City now believe that last summer's £118m investment in the squad has removed the need for another large scale influx of players. Quality rather than quantity will be the blueprint.
City face Portsmouth at Eastlands on Sunday with Mancini warning his players that the visitors will not be distracted by the financial problems that are currently engulfing the south coast club.
Mancini said: 'It is a dangerous situation for us because the Portsmouth players will not be thinking about the club's situation when they are on the pitch. We must pay a lot of attention to this game because it is an important one after the United match.'