Pellegrino has confirmed Southampton are still "pushing" on a deal to bring Promes to St Mary's.
The Argentine says any potential move is still a number of days away meaning that negotiations could roll on right up to Deadline Day on January 31.
Pellegrino said: "Quincy Promes is one of the players that we have been following for a few months. The market is too difficult, we wait until the end and keep pushing."
Meanwhile, Southampton legend Matt Le Tissier believes the club is right behind Pellegrino.
"If it goes the wrong way, it is not looking good..."