City compete in the FA Cup final on Saturday in what could be current boss Roberto Mancini's fourth major honour at the club after the 2010-11 FA Cup, last season's Premier League title and the 2012 Community Shield.
However, City's below-par defence of the Premier League title this season has left Mancini's position tentative, with rivals Manchester United having comfortably wrapped up the league in April.
In contrast, former Villarreal boss Pellegrini has rebuilt his career at Malaga after underachieving at Real Madrid in 2009-10 and has been linked with a series of elite jobs, including Chelsea (12/1), Arsenal (20/1) and PSG (12/1).
Sky Bet's Chris Spicer said: "We're not sure where the Pellegrini to City rumours stem from, but we've had no shortage of bets from serious punters, even at odds-on.
"We've had no choice but to shorten the price to protect ourselves in the event of another shock announcement from Manchester. Incidentally, Jose Mourinho is a distant second favourite at 16/1."