The Netherlands international was heavily linked with a move to Anfield in the off-season, but ended up staying at Southampton.
His team visit Jurgen Klopp's men in the Premier League on Saturday after a slow start to the campaign.
Pellegrino has no doubt Van Dijk, 26, is focused on Southampton after making just five league starts so far this season.
"I don't think it will be difficult because Virgil is focused 100 per cent on our team and is training well," the Argentinian said.
"He wants to improve his performances because obviously he was injured and he didn't play any games [earlier in the season].
"Obviously we cannot control the market and every single transfer window clubs are looking to buy our players.
"It's no secret that sometimes players are distracted, but it's normal."
Liverpool sit fifth in the table ahead of the visit of Southampton, who are 13th.