The Daily Mail says there is increasing anxiety, with executives questioning for the first time whether they made the right choice when replacing Mark Hughes with the enigmatic Italian at the end of last year.
City lost 3-1 after extra time at Stoke City on Wednesday to crash out of the FA Cup. That came on the back of an exciting but disappointing Carling Cup semi-final defeat by Manchester United at the end of last month.
The only challenge that remains is for Mancini's City to try to qualify for the Champions League. Such an achievement would undoubtedly secure Mancini's future but anything else is increasingly likely to see him on his way back to Italy after six months.
City executives are also disturbed by the mundane, unambitious football that has recently begun to characterise his reign.
Since Mancini arrived at the club, only three of his 15 games have offered any real encouragement of a bright future. These were a 3-0 win at Wolves, a 2-1 Carling Cup first-leg win over neighbours United and a 4-1 home win over Blackburn. The rest, even the victories, have been mundane and unconvincing.