Danjuma has been linked with a return to English football in 2023 with former side Bournemouth registering an interest in recent weeks.
Transfer expert Fabrizio Romano has previously stated how Danjuma sees his future back in England with Everton also tipped as the front runners for him this month.
However, there could be up to five Premier League clubs interested in a deal, with the Daily Mail claiming Forest have now entered the race for the Dutch international.
Danjuma has netted 22 goals in 51 appearances during his time with the Yellow Submarine and Forest will challenge for him, if they can agree a fee with Villarreal.
Forest signed over 20 new players ahead of their long awaited Premier League return last summer but head coach Steve Cooper is still looking to strike the right balance in his squad.