The Citizens head into this weekend's derby meeting with Manchester United on the back of a string of bad results in three different competitions, most recently Tuesday night's 2-0 defeat against Newcastle United which saw the holders exit the League Cup.
City's fortunes in the Champions League also hang by a thread, while they trail Premier League leaders Chelsea by six points.
"I think City are really struggling," Marsh told talkSPORT. "I think he will get the sack. There is every chance, if this carries on, that Pellegrini will be out, the same as [Roberto] Mancini was. Mancini won the Premier League and the following year finished second and he was sacked.
"If Pellegrini carries on like this, and Man City don't win the league or get to the final at least of the Champions League, which is looking dodgy as well, I think Pellegrini is sacked. He could go earlier. I think it is on a really fine balance now.
"People that are close to the club that I know are all saying that the owners have put in £175m and they are struggling. I think the owners are probably thinking if we get knocked out of the Champions League and if we end up third or fourth or fifth in the Premier League - which I don't think will happen - then I think Pellegrini is out early."
Marsh spent four years at City, scoring 36 goals during his time at the club.