The struggling Premier League club have money to spend thanks to the £75m sale of Virgil van Dijk to Liverpool and according to reports in England on Wednesday, Pellegrino looks set to make the Argentine forward his first January signing.
The 'Saints' have struggled in front of goal this season, netting only 24 times. Top-scorer Charlie Austin picked up a muscle injury in December and will be sidelined until the end of February whilst Shane Long has only scored once since February 2017. Italy international Manolo Gabbiadini has also flopped despite his promising start last season.
Carrillo has made 65 Ligue 1 appearances for Monaco, finding the back of the net on 15 occasions, since moving from Estudiantes in 2015. However, the 26-year-old has had to compete against the likes of Radamel Falcao, Adama Diakhaby and Keita Balde Diao which could stand him in good stead for the Premier League.
His Argentinian nationality will link up well with Pellegrino too, as Southampton find themselves in the relegation zone, one point from safety, and in desperate need to string some results together following their 1-1 draw to Tottenham on Sunday.