The Netherlands international handed in a transfer request over the summer amid strong speculation linking him with a move away from St Mary's.
He captained Saints under former boss Claude Puel last season, but current manager Pellegrino was coy on whether the Dutchman would reclaim the armband from midfielder Steven Davis.
"For me the captain is something that the team-mates decide and something that you have to deserve," said the ex-Alaves chief.
"Now, when he's not playing, you cannot put the captain on someone that is not playing, but obviously Virgil was one of the leaders of the squad."
The ex-Celtic star has not featured in any of Saints' five matches so far this campaign due to the uncertainty over his future, and has not played competitively since suffering a foot ligament injury against Leicester in January.
But he did play in an Under-23 game on Monday evening - a 4-0 defeat to Aston Villa - and could be a surprise inclusion for the Premier League fixture at Crystal Palace on Saturday.