The 29 year old January signing is expected to finalise a move to the Turkish outfit in the coming hours.
Onuachu, a Nigerian international, netted 16 goals in his last 13 Belgian Pro League games for Genk before signing for Saints under former manager Nathan Jones.
He is yet to score a goal for the St Mary’s side and is not part of boss Russell Martin’s plans, making just one substitute appearance in the EFL Cup.
Genk had been attempting to re-sign Onuachu but the Belgian window has already closed and no move is possible.
Onuachu is set to complete his medical at Trabzonspor ahead of their transfer window closing on September 15
Onuachu cost over £15million to sign from Genk, while club-record signing Kamaldeen Sulemana also joined on deadline day but remains at the club.
At the time, Jones said: “Paul is a significant signing for us and completes what has been an extremely positive month in terms of recruitment.
“He’s a handful to play against, has got a tremendous record throughout his career and he’s also someone who brings great experience with him, so he’ll be a really positive addition to the squad
Jones was sacked just weeks later following a 3-0 defeat at Brentford and a 2-1 home loss, after going ahead, to 10-man Wolves.
Onuachu made his substitute debut in West London and started the loss versus Wolves, which saw former Saint Mario Lemina sent off.
Onuachu fell out of favour under Jones replacement Ruben Selles, who had been an assistant coach throughout the season.
The Nigerian started a win at Chelsea before struggling in the definitive 1-0 defeat at Leeds United. He then missed out on victory against Leicester City that followed.
Onuachu made just one more start and a handful of substitute appearances as Saints failed to win another match for the rest of the season, finishing bottom of the league
Onuachu was also left out of the Nigeria squad for this month’s international break, with Saints forward Joe Aribo still called up.
It is unclear if this is due to Onuachu’s lack of involvement at club level or in order to fully complete this move to Trabzonspor ahead of the deadline closing.
Trabzonspor also signed fellow January flop Mislav Orsic from Saints this summer but the Croatian international has been ruled out of action by a pre-season injury.
The Turkish side last week added Arsenal winger Nicolas Pepe, 28, who joined the Gunners from Nice for £72million only four years ago.