The Championship side are looking for a permanent appointment after parting company with Dougie Freedman.
The Championship club have been without a permanent boss since Dougie Freedman was sacked back in March, with Paul Williams taking over until the end of the season.
And after failing in their bid to land Gus Poyet, the Mail reports that the club's hierarchy ideally want a manager that has an attachment to Forest.
While much more familiar names like Nigel Clough and Martin O'Neill have been linked, the Mail suggests that Forest are also considering a move for Wright, who enjoyed an unspectacular spell at the City Ground.
Despite being with the side for four years, the Northern Irishman made just 11 league appearances. But while his playing days were uninspiring, his managerial career has been a lot more impressive.
After starting out in the dugout in his home country, St Johnstone gave him a chance in 2013, where he has arguably done a fantastic job.
With one game to go this season, the Saints have secured fourth spot in the Scottish Premiership for a second consecutive year to go along with the sixth place finish they achieved during his first campaign in charge.
He also guided them to Scottish Cup glory in 2014, so while it would be a gamble if Forest were to turn to him, his track record suggests that he has the potential to do well for the club.