Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The move comes after speculation linking the former Real Madrid chief with the top job at the Etihad Stadium in recent days.
City manager Roberto Mancini is under pressure as his side trail rivals Manchester United by 12 points in the Premier League title race and their European campaign was over before Christmas.
Jose Mourinho has also been linked with the City job and sits second in Sky Bet's next manager market at 5/1.
Sky Bet football trader Chris Spicer said: "It would appear unkind to replace Mancini but clearly the owners have expectations that match their lofty investments.
"Pellegrini may not be a huge name amongst City fans but it is hard to ignore the success he is achieving this season with Malaga. The Chilean has had a spell in the big time before, in his short time at Real Madrid in 2009.
"Sky Bet customers were aware of rumours early on this afternoon and did some damage at 20/1 before we were forced to change the odds dramatically. A quick appointment isn't necessarily what City will prefer but sources suggest they may appoint him at the end of the season."