Keane wrote in the Sun on Sunday: "City have made progress this season but they have been in five competitions and it looks like they’re going to end up empty-handed.
"City’s owners have shown with Mark Hughes they are not a patient lot. So you could see them deciding that the progress hasn’t been quick enough for the investment they’ve put in — especially when they’ve thrown away a five-point lead.
"Mancini has been around long enough to know he is at risk. He was sacked by Inter after winning seven trophies in four years.
"I don’t like to see any manager lose his job but Mancini hasn’t done himself any favours at times.
"After defeats to Everton in January and Sporting Lisbon in March, Mancini admitted he had underestimated the opposition.
"That’s one of the biggest mistakes you can make in sport and I was shocked that he confessed to doing it not once, but twice.
"We all like a bit of honesty in the game but there will be enough people criticising without leaving yourself open to attack like that."