The 24-year-old struggled to convince Mikel Arteta in the first half of the 2021-22 season and also endured a frustrating loan spell with Roma under Jose Mourinho.
Maitland-Niles failed to score or provide an assist in 12 games for the Italian side in all competitions, and he was an unused substitute in 10 of Roma's last 12 Serie A matches.
Maitland-Niles will soon return to the Emirates for the pre-season period, but it remains to be seen if he has a future at the club under Arteta.
According to the Daily Mail, Forest boss Steve Cooper is therefore keen to take advantage of Maitland-Niles's situation by offering the England international an escape route.
The report adds that Forest view the versatile Maitland-Niles as an ideal replacement for Djed Spence, who has headed back to Middlesbrough following his successful loan spell.
Maitland-Niles only has 12 months left to run on his contract with Arsenal, who could be forced to sell him on a cut-price fee or risk losing him on a free transfer in 2023.
The Englishman has spent 19 years at the club since joining as a schoolboy in 2003, and he has since scored three goals and set up eight more in 132 appearances for Arsenal's first team.
Maitland-Niles has won three FA Cups and two Community Shield crowns with his boyhood club, and he also became world champion with England's Under-20 side in 2017.
However, the midfielder started just two Premier League games in the first half of the 2021-22 season and did not play a single minute in the top flight in December before heading to the Stadio Olimpico.
The Tricky Trees have already broken their transfer record since returning to the Premier League, with Taiwo Awoniyi joining from Union Berlin for a £17.5m fee.
Forest are also expected to conclude a loan deal for Manchester United goalkeeper Dean Henderson, who will arrive for the 2022-23 season to replace wantaway number one Brice Samba.
Samba has allegedly informed Forest that he will not be extending his stay at the club beyond the summer of 2023, and the 28-year-old is thought to be heading for Ligue 1 outfit Lens.
Forest's first game in the Premier League for 23 years sees them take on Newcastle United at St James' Park on August 6.