The Gunners moved to sign the Italy international during the January transfer window with Chelsea having then been open to a cut-price deal.
Although Arsenal missed out on silverware during the second half of the campaign, Jorginho proved to be a valuable option, making 11 starts and six substitute outings in all competitions.
However, the 31-year-old has only played a limited amount of minutes during pre-season, never accumulating more than 45 minutes in a single game.
In total, 114 minutes came from four fixtures, while Jorginho did not participate in Sunday's Community Shield triumph over Manchester City due to injury.
As it stands, the perception is that Jorginho could prove to be a dependable squad option at the North Londoners with Champions League football back on their schedule.
Nevertheless, according to Trtspor.com, Fenerbahce have Jorginho on their radar courtesy of a request being put in to depart Arsenal.
The report suggests that Jorginho has informed club officials of a potential proposal coming onto the table from the Turkish giants.
Having only penned a short-term contract upon his arrival earlier in the year, Jorginho has less than 12 months remaining on his contract.
Earlier in the summer, the suggestion was that Jorginho would look to remain at Arsenal for 2023-24 courtesy of a move back to Italy not coming to fruition.
That said, it now appears that Fenerbahce has enquired about his availability as they bid to make yet another eye-catching signing before the closure of the market.
Dusan Tadic and Edin Dzeko have left Ajax and Inter Milan to move to the Sukru Saracoglu Stadium, while substantial fees have been spent on Udinese defender Rodrigo Becao and Dynamo Moscow midfielder Sebastian Szymanski.
Ismail Kartal's side are currently preparing for the new Super Lig season and bidding to qualify for the Europa Conference League group stages.