Southampton are fast closing in on the signing of Carrillo, who worked with Pellegrino at former club Estudiantes, with an agreement in the region of £19m understood to have been reached with Ligue 1 champions Monaco.
"We are working really hard to try and move forward," he told reporters at his weekly presser. "Hopefully we can have some good news tomorrow, but still nothing has happened.
"We are confident. I think the player wants to come, to be part of our squad but the most important part of the negotiations are still there so we have to continue to work.
"We are looking for someone who can replace Charlie or the quality of Charlie [Austin]. Obviously it is not the same player, but this is our target now. I don't know if he will be ready [for Brighton] because we have to test the player."
Carrillo has made 22 appearances for Monaco this season, though just two of those have been starts.