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