The Post claims that former Brighton & Hove Albion boss Oscar Garcia is one candidate, though the identity of the other is not disclosed by the report.
However, the second candidate is not thought to be Martin O'Neill, despite the Reds harbouring faint hopes of appointing their popular former winger.
If true, Garcia would be the second former Seagull to be targeted by Forest this summer, after Gus Poyet, who opted for Real Betis instead.
The Spaniard replaced Poyet at the Amex Stadium in 2013 and led Brighton into the Championship play-offs.
After losing to Derby County in the semi-finals, Garcia resigned before returning to Maccabi Tel Aviv, with whom he won the Israeli championship in 2012-13.
However, three months later he was back in England, taking over at Watford until ill health forced him to step down after two weeks in charge.
Garcia returned to management with Austrian side Red Bull Salzburg in December 2015, and led the team to the league and cup double this past season.
The report reiterates that O'Neill will not discuss his future until the Republic or Ireland's participation in Euro 2016 is over, and Forest will continue their search in the meantime.