The pre-season title favourites lost 1-0 at Sunderland and as a result, Mancini has been cut to 9/2 second favourite from 8/1 to be the next top-flight boss to lose his job - behind Reading manager Brian McDermott, who is 7/4 favourite.
Trader Chris Spicer said: "While the City hierarchy haven't previously proven to be trigger-happy, they've looked well short of the side that won the title last season and are finally being found out.
"With their Champions League campaign ending in misery, the Premier League is surely a must with such a talented squad at Mancini's disposal, so we deem him to be under genuine pressure now."
Aston Villa suffered another heavy defeat on Boxing Day - this time losing 4-0 at home to Spurs following the weekend's 8-0 mauling at Chelsea - and now Paul Lambert can be backed at 6/1 in the sack race.
Saturday 29th December 2012
Sunderland V Tottenham Aston Villa V Wigan Fulham V Swansea Man Utd V West Brom Norwich V Man City Reading V West Ham Stoke V Southampton Arsenal V Newcastle
Sunday 30th December 2012
Everton V Chelsea QPR V Liverpool
Tuesday 1st January 2013
West Brom V Fulham Man City V Stoke Swansea V Aston Villa Tottenham V Reading West Ham V Norwich Wigan V Man Utd Southampton V Arsenal
Wednesday 2nd January 2013
Chelsea V QPR Liverpool V Sunderland Newcastle V Everton
Source: Manchester City MAD