The Saints have money to spend this month following the £75m sale of Virgil van Dijk to Liverpool.
Monaco's Guido Carrillo is among those to have been linked with a move to St Mary's as the out-of-form Premier League club look to provide support for leading scorer Charlie Austin - who is currently injured - in the final third.
Pellegrino has said that the club's "priority" is to bring a new centre-forward to the club this month.
"I think the priority is to try to help the final third, because Charlie [Austin] will be out and we don't have his profile in the squad. He is one of our priorities," Pellegrino told reporters.
Southampton will enter Saturday's Premier League clash with Watford having not won in the top flight since the end of November.