In comments reported by the Daily Record, former Celtic and Premier League defender Alan Stubbs has insisted that he cannot see why Brendan Rodgers would choose to leave the Hoops for the vacant job at Southampton.
The Saints are searching for their new manager with just eight games left in the season after Saturday's humiliating 3-0 defeat to Newcastle left the south coast club just one place and one point above the bottom three in the Premier League.
Pellegrino was sacked and The Scottish Sun soon suggested that Southampton would try their luck with a move for Celtic boss Rodgers, who has enjoyed a hugely successful spell at Parkhead in the wake of the disappointing end to his time with Liverpool.
But Stubbs admitted that he can see no reason why Rodgers would want to make the move to St Mary's, suggesting that a role such as the Arsenal job is on the level that Rodgers should be looking for.
“I know they’ve signed the likes of Wanyama, Forster and van Dijk for decent sums of money but Celtic got three good deals out of that.
“It is an entirely different ball game for Southampton if they want to try to land one of the most successful managers in Celtic’s history. The bottom line is Celtic are a much bigger club than Southampton.
“He’s being linked with Southampton one minute and in the same breath he has been linked with a switch to Arsenal. If it was an Arsenal then I would be more concerned if I was a Celtic fan," he went on to add.
Luckily for Bhoys fans, it does appear that they will not need to worry about their manager receiving an approach right now as BBC Sport recently reported that Mark Hughes is in talks with the Saints about succeeding Pellegrino.
Of course, the deal could fall through and Southampton may need to pull something special out of the bag to appease understandably-disgruntled supporters - so perhaps there may be an outside chance that they could still consider putting Stubbs' comments on Rodgers' decision to the test.