After avoiding relegation on the penultimate weekend of the season on their return to the top flight, Steve Cooper will be looking to strengthen his squad to maintain their place in the Premier League again next year.
Turkish newspaper Takvim claims that Forest are interested in Akturkoglu, with a bid already said to have been made, which has been rejected by his club Galatasaray.
After a stellar season which saw Akturkoglu help Galatasaray to the Super Lig title, the 24-year-old contributed to 24 goals as his side finished eight points clear of Fenerbahce at the top of the standings.
Akturkoglu is now a regular for Stefan Kuntz's Turkey side, and featured in both of their June internationals, with a bid of around £9.5m said to have been declined.
A winger is evidently on the radar for Steve Cooper this summer, as The Guardian have also claimed that Hudson-Odoi is a player Forest are looking at.
However, they will face competition from AC Milan and Fulham for the 22-year-old who is out of contract in 12 months time.
Hudson-Odoi endured a frustrating season on loan at Bayer Leverkusen where made just 15 appearances, failing to find the net.
Chelsea are said to want around £15m for the wide man who came through their youth ranks, and will hope to get his £120,000-per-week wages off the bill.
The fee and wages combined may make the deal slightly difficult for Forest, but they could recoup some of that money should they sell Emmanuel Dennis in this window.
The Telegraph claims that Dennis has been transfer listed at the City Ground after failing to make much of an impact in his first season in Nottingham.
After arriving from relegated Watford last summer, the Nigerian international made just six Premier League starts, scoring twice, failing to get regular playing time ahead of the likes of Brennan Johnson and Taiwo Awoniyi.
The report claims clubs in Russia and Saudi Arabia are interested in Dennis, who could leave for as much as £20m, and could help finance a move for either Akturkoglu or Hudson-Odoi.