Southampton are looking to bring in a new striker before the end of the current window.
The Saints €12m bid for Onuachu was rejected by Genk, according to getfootballnewsbene.com.
The Limburgers want to keep the 28-year-old for their title challenge.
Genk are currently nine points clear at the top of the Belgian Pro League.
The Nigeria international has scored 14 goals in 18 games for the Limburgers this season.