Russian side Spartak Moscow have reportedly knocked back a £25m bid from Southampton for Dutch international winger Quincy Promes.
The Saints are keen to inject some proven quality out wide during the final throes of the winter window and were hopeful of bringing in the 26-year-old.
Southampton are said to have pushed ahead with a formal offer, which has been met by resistance from Spartak as they are reluctant to sell their prized asset.
According to Sky Sports News, the south coast side are now debating whether to make another bid before the close of play on Wednesday.
Asked at his pre-match presser on Monday about the possibility of some movement, Pellegrino said: "It's possible. It's probable. We never know but we have got some interest that maybe some of our players can go on loan but depends on the other club too.
"In the middle of negotiations there are money and budgets and after in the opposite way the same. We want to bring a player but it is difficult for us."
Southampton, currently 18th in the Premier League standings, signed striker Guido Carrillo from Monaco earlier this month for a club-record fee.