Van Dijk handed in a transfer request at St Mary’s in August, and spent pre-season with the Saints’ Under-18s, as he pursued a move to Liverpool.
But the Dutchman has now returned to Pellegrino’s squad, coming off the bench in Saturday’s 1-0 win away to Crystal Palace for his first senior appearance since January.
According to the Times, however, Pellegrino “would have happily sold Van Dijk during the summer to raise funds to strengthen his squad elsewhere.”
The ex-Reds assistant manager was ultimately “overruled by the Southampton board,” leading to the centre-back’s reintegration this season.
But speaking after his side’s victory at Selhurst Park, Pellegrino hinted at a possible move in January.
“For me I have got this group of players and we try to push them, to help them, to work with them, to improve every single day,” he told reporters.
“We never know how the market will be in January because we can bring some players [in], because every single squad can improve.
“We have got people who are working to improve our squad all the time, and for the other teams it is the same. They will push to bring the best players.
With Liverpool conceding another sloppy goal in Saturday’s 1-1 draw at home to Burnley, the need to sign another centre-back in the summer was once again underlined.
Ahead of that clash, Klopp insisted he and his recruitment staff had watched a host of alternatives “500 million times.”
The German suggested that he turned down the prospect of signing Colombia international Davinson Sanchez, who ultimately join Tottenham from Ajax, as well as Napoli’s Kalidou Koulibaly.
Currently, only Matip looks settled in the role, with the 26-year-old the only player to play every minute of every game for the Reds so far this season.
Lovren and Klavan have rotated alongside Matip, with neither looking wholly comfortable, and a January move for Van Dijk would certainly be welcomed on Merseyside.