Salah, 34, has been a free agent since leaving Liverpool, where he tore up the final year of his contract early and finished his time at Anfield with 255 goals in 435 appearances, third on the club's all-time scoring list, having helped win eight major trophies including two Premier League titles and the Champions League.
A move to Beşiktaş had appeared close before collapsing at the last moment amid financial disagreements over his representatives' commission demands, with the Istanbul club's sporting director later saying they would not budge on terms unavailable to other players.
According to Turkish journalist Yağız Sabuncuoğlu, Trabzonspor's offer would guarantee Salah roughly €34m in salary across two seasons, alongside a discussion over a share of shirt sales reported to be in the 20-25% range; if accepted, it would make him the highest-paid player in Turkish football history.
Trabzonspor president Ertuğrul Doğan has pushed back on suggestions a deal is already done, telling A Spor: "There is a lot being said, but there is no agreement with Mohamed Salah.
"There are no arrangements for him to travel to Trabzonspor tomorrow. Of course we would wish for that, but the truth is that there is no agreement at this moment."
Saudi Arabia has repeatedly been mentioned as an option for Salah in recent transfer windows too, and journalist Gianluigi Longari reports that Al Ittihad have now considered the Egyptian as a contingency, should Moussa Diaby leave the club; the 27-year-old has been linked with a return to Bayer Leverkusen.
For now, though, Trabzonspor appear best placed to land Salah once he gives his final answer. The club finished third in the Süper Lig last season and will play in the Europa League play-off round, which begins in two weeks, meaning Salah could conceivably be involved from the very start of the campaign were terms to be finalised in time.