On-loan for the season, Onuachu scored 17 goals and made four assists in 26 games with Trabzonspor.
Trabzonspor are eager to keep the centre-forward, but the decision is up to Southampton, as there is no buy-out clause written into the contract.
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Onuachu himself has previously hinted at a return to Southampton, where there is a prospect of Premier League football.
His contract in England expires in June 2026.