The Saints are looking to strengthen their squad before today's 11pm deadline, as they attempt to avoid relegation from the Premier League.
Rennes winger Kamaldeen Sulemana is allegedly set to sign for the club, and he could be joined by Onuachu.
According to the Daily Mail, Southampton are close to agreeing to an £18.5m deal for the Genk forward, who was also believed to be a target for Everton.
Onauchu has scored 85 goals and provided 10 assists in 134 appearances for Genk, but he is now expected to leave the Belgian club to sign a three-year deal with Nathan Jones's side.
In a separate update from journalist Fabrizio Romano, Sulemana and Onauchu are undergoing medicals ahead of their respective moves.
Onuachu stated in December 2022 that he was open to the prospect of a transfer despite being happy to remain at Genk.
The 28-year-old told HLN: "I score a lot, I like being here. But: if there is an interesting offer this winter or next summer, we will look at it together with Genk. Because I still dream of playing in a big league."
The Nigeria international will join a Southampton side who are currently bottom of the Premier League table and two points adrift of safety.
Should the deal be completed before the transfer deadline, Onuachu could make his debut in Saturday's Premier League meeting with Brentford.