Pellegrino told the press on Saturday that the Dutchman was fit and available for selection, but opted to leave him out for the second game running against Spurs.
This comes amid claims that the defender is closing in on a big-money move to Premier League leaders Manchester City.
English publication 'The Telegraph' reports that the 26-year-old is on the verge of joining Pep Guardiola's side in a £60m move when the transfer window reopens in January.
Guardiola tried to sign a centre-back in the summer but failed with a Deadline Day move for West Brom's Jonny Evans, who was once again linked with a move to the Etihad in recent weeks, along with Real Sociedad's Inigo Martinez.
City's lack of depth at the back was recently exposed when injuries to captain Vincent Kompany and John Stones forced City to field Eliaquim Mangala at the back, a player that the club were keen to sell on during the summer. That is a situation that Gurdiola is keen to avoid a repeat of, hence the interest in Van Dijk.
The City boss has stressed his desire not to make signings for the sake of it, but sees Van Dijk as a valuable long-term option and believes he would be a good fit for City.
The former Celtic defender would also add physicality at the back, with his 6ft 4in frame allowing him to dominate opposition strikers.
Liverpool and Chelsea are both known to hold an interest in Van Dijk, but if the latest reports are to be believed, he will be a City player sooner rather than later.