Pellegrino, who leaves with the third worst Southampton managerial record in the Premier League, appeared to be bracing himself for the sack after last weekend's loss to Newcastle as he admitted he "observed some players who gave up".
The Argentine was relieved of his duties as manager after going 17 games with just one win.
Like Hughes, Silva was sacked by a Premier League club in January - in his case Watford - and he has also been linked with a move back home to Portugal to take over at Benfica next season.
Welshman Mark Hughes was firming as the bookmakers' favourite to replace Mauricio Pellegrino as the south coast club's manager. "It's now time to move on, appoint a new manager, and get out of the trouble we are in at the moment".
"The club will look to appoint a new management team as soon as possible, with the search for a replacement already underway", Southampton said.
That salary and likely seven-figure compensation figure would not deter Saints, who face a huge fight to maintain their top flight status.
So they hired Pellegrino, and nine months on they must be regretting their decision.
It is added that former Hull and Watford boss Silva "is not understood to be in consideration" for the post, while ex-West Ham manager Slaven Bilic "is not prominent on the immediate shortlist".
The former England boss is THE anti relegation specialist, becoming the firefighter to extinguish all relegation threatened Premier League blazes, having never been previously relegated in his career.
As the paper points out "given the club's perilous position they will struggle to attract a leading manager", increasing the likelihood that the Saints will go marching into the Championship at the end of the season.