It has been reported that the Turkish club are in talks with Arsenal over the transfer of the Egypt international midfielder.
Talks are at an advanced stage, according to the report, which has added that Trabzonspor are ready to offer €1.5 million (£1.36 million) per season to the 28-year-old.
Elneny has been on the books of Arsenal since 2016, but the defensive midfielder spent the 2019-20 campaign on loan at Besiktas.
According to WhoScored, the former Basel star scored one goal and provided three assists in 27 Super Lig matches, and played six times in the Europa League for Besiktas this past season.
If Trabzonspor are reportedly so keen on signing Elneny, then he should seriously consider a move to the Turkish club.
Trabzonspor finished second in the Turkish Super Lig in 2019-20, and they could be challenging for the title again next season.
Meanwhile, according to AllNigeriaSoccer, 18-year-old Nigerian Ryan Alebios has signed his first professional contract with Arsenal.
The report has claimed that the teenager has signed a two-year contract with the Gunners, with the North London outfit holding an option to extend by a further two years.