Saints want to add to their attacking options on deadline day and on Monday night put in an improved offer for Onuachu.
The striker is keen to make the move to England as he dreams of playing in the Premier League and Southampton have a four-and-a-half year contract ready for him to sign.
Genk do not want to lose Onuachu though as he is a key man in their title charge.
Talks are continuing to take place between the two clubs, but according to Belgian daily Het Laatste Nieuws, little progress has been made.
Discussions are continuing and it remains to be seen if Southampton can convince Genk to sell today.
Ounachu meanwhile reported as usual for Genk training this morning, showing little sign of being unsettled by Southampton’s interest.
He wants to make the move, but has not taken the step of skipping training to put pressure on Genk.
