The Mirror says if Pellegrino fails to lift Saints out of the bottom three in the next seven days, then the axe will fall and Hughes will get the call.
Pellegrino faces a win-or-bust derby against Brighton at St Mary's on Wednesday night, with another crucial relegation battle at West Brom to follow on Saturday.
The worried Southampton board are expecting at least four points from the clashes and, if Pellegrino doesn't deliver, they won't be afraid to act.
They will attempt to bring in Hughes who spent two years on the south coast as a Saints player between 1998 and 2000.
Although he was sacked by Stoke earlier in the month, there is a belief within the Southampton hierarchy that he has the experience to help guide the club to safety.