The club captain has been reintegrated into the senior squad having been training on his own after handing in a transfer request at the start of August.
Van Dijk wanted the Saints to take up the interest from Liverpool, who issued a public apology in June following allegations of an improper approach for the Dutchman.
The player has been out of first-team action since sustaining a serious ankle injury in January but will feature for Southampton's second string against Aston Villa at the Bescot Stadium.
"Virgil is coming from a long period of time without playing a game. This is my concern right now," Pellegrino told Sky Sports News.
"He will play Monday in the reserve team. We try to help him to be ready to help the team. He was training well this week. Now everything is normal."
Van Dijk has made 68 appearances for Southampton since his 2015 move from Celtic.