Media in Turkey have reported that the two clubs have agreed on a deal worth a total of €5million (£4.2m) but this is thought to be wide of the mark.
Onuachu, 31, has been pursued by the Turkish club for 12 months since he scored 17 goals in 23 matches on loan there in the 2023/24 season.
Saints rejected bids Trabzonspor worth £5m last summer but the Nigerian international is set to enter the final year of his contract at St Mary's.
As set out by Trabzonspor boss Faith Tekke last month, the Super Big outfit have returned to the negotiation table to try and sign Onuachu.
Turkish reports suggesting Trabzonspor and Saints have reached an agreement for Paul Onuachu at €5million are not true. They are interested and negotiations are ongoing but Saints don't want to sell at that price and anticipate talks could rumble on for a while again.#SaintsFC
— Alfie House (@AlfieHouseEcho) June 8, 2025
However, Saints are reluctant to sell at the price currently discussed and anticipate that talks could rumble on into the summer months again.
Onuachu signed for Saints in a deal worth around £15million in January 2023 but only established himself as a regular player under Ivan Juric.
He battled a persistent ankle injury last campaign and his managers had admitted he struggles to play week-in week-out at his top level.
As a result, Saints could cash in ahead of a physically taxing Championship season and he retains interest from clubs due to his prowess in front of goal.
He has scored 83 goals in league competition since the start of the 2020/21 season, and was Southampton's 2024/25 top scorer with four league goals.
Onuachu made 25 Premier League appearances last campaign, in addition to three appearances in the club's domestic cup competitions.