Monaco have rejected a £17.6m offer from Southampton for striker Guido Carrillo, Sky Sports News understands.
Sky Sports News reported earlier this month that the Saints were keen to sign the 26-year-old, who previously worked with boss Mauricio Pellegrino in their native Argentina.
Carrillo has made 22 appearances this season but just two of them have been starts in Ligue 1. He has scored 20 goals in over 50 appearances for Monaco since signing from Estudiantes in 2015.
Southampton, who sit outside the Premier League relegation places by just a point, are seeking a target man to play alongside Charlie Austin when he returns from injury.
Saints have money to spend following the £75m sale of centre-back Virgil van Dijk to Liverpool, although the fee is to be paid in instalments over the period of his contract.
Speaking on Friday, Pellegrino admitted Southampton tried everything to sign Theo Walcott and suggested Monaco forward Carrillo is on the club's radar, but maintained he does not want to discuss players who are contracted to other clubs.
"He's a player I know and the club know," he said.
"But I will not talk about someone else who is not here. The player is either yours 100 per cent or nothing. One small detail can change the negotiation.
"If we bring people here it is because we feel they will improve the squad."