City face Wigan in the FA Cup final on Saturday as current manager Roberto Mancini seeks another major honour at the club having won the cup in 2011 and last season's Premier League title.
However, City's below-par defence of that title this season, with rivals Manchester United wrapping up the league in April, has left Mancini's position under threat.
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 three-figure 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."