The 24-year-old has seen his contract with Red Bull Salzburg terminated at the weekend.
As a result, he is a free agent and can sign for any team, with Forest assessing his situation.
Per HITC, they will face a lot of competition, with Aston Villa, Wolves and West Ham United also keen.
French outfit Marseille, Anderlecht in Belgium, and Inter Milan are also circling.
In a statement, Red Bull Salzburg said: “FC Red Bull Salzburg and Oumar Solet have parted ways. The 24-year-old Frenchman's contract, which still had a year to run, has been terminated early by mutual agreement.
“The center-back joined our Red Bulls at the start of the 2020/21 season from Olympique Lyon. Over his four seasons in Salzburg, Oumar Solet made a total of 106 appearances (with four goals and five assists) - winning three league titles and an Austrian cup.
“We wish Oumar Solet all the best for his future!”