City do still have two games in hand but manager Roberto Mancini is under pressure to justify the massive amount of money spent on the Blues squad, even if he was only responsible for spending a small fraction of it.
But Davies feels the effort is doomed to failure.
"I don't think City will be challenging for the top four," he told the Manchester Evening News.
"The top six to eight sides are all great teams spending good money.
"But I think City might miss out on the Champions League this year."
Indeed, Davies does not feel Bolton are without hope, even though they are precariously placed just above the relegation zone and are without an away win since September.
"City have some great players but sometimes when you have all those superstars it is hard to get that team spirit," he said.
"When their new manager came in, you expected a reaction from the players and they won their first three or four games.
"But obviously it has settled down a bit now and maybe they are not as keen to impress."
Barclays Prem To Be in Top 4 Win Outright: Man City 6/5