The midfielder only arrived at the City Ground in January, but after seven months, his time at the club is set to be put on pause.
Shelvey made just six starts after joining halfway through last season, and did not feature after he was allegedly dropped before Forest's trip to Liverpool in April.
The Telegraph now claims that Shelvey will leave the club for the season at least, to join Rizespor.
The Turkish club are fifth in the Super Lig, two points adrift of league leaders Fenerbahce.
Shelvey is contracted at Forest until 2025 after signing a two-and-a-half year deal with the club at the start of the year.
With having just six months left on his deal at Newcastle United, Forest paid £5.6m for the 31-year-old, who asked to leave St. James' Park for a fresh start.
Rumours surfaced that Shelvey and manager Steve Cooper had fallen out over the decision to drop the player from the squad though.
Shelvey was then told to stay at home with the manager displeased over his conduct and performance in training.
That led the manager to come out publicly and state that there is "no ill feeling between the pair" and that injury was also a factor in Shelvey not being picked.
The Turkish transfer window does not close until Friday so there is still time for the deal to be completed without much fuss.
Shelvey would become the next Englishman to make a move to the Super Lig in recent years, following the likes of Dele Alli, Aaron Lennon and Nathan Redmond.
Juan Mata, Hakim Ziyech and Wilfried Zaha have also swapped the Premier League for the Super Lig in the recent past, all joining Galatasaray, while Tottenham Hotspur duo Tanguy Ndombele and Davinson Sanchez joined the current Turkish champions last week.