Chelsea sacked Tuchel earlier this season and it was recently claimed that two Premier League sides have failed with approaches to land him.
The identities of the Premier League sides has not become known, but Keys thinks Nottingham Forest may well have been one of them.
And the former Sky Sports anchor is of the view that if Tuchel was open to taking charge at the City Ground then Nottingham Forest would have quickly sacked Cooper.
“Forest. Why not? If they could have got him they would have sacked Steve Cooper”, Keys said on the Keys & Gray podcast when discussing the two unnamed clubs.
“He’s not [going to Forest] but there’s no harm in asking.”
Cooper recently signed a new contract at Nottingham Forest, but it has not handed their prospects on the pitch a boost.
Nottingham Forest lost to Wolves on Saturday and are rock bottom of the Premier League table with only one win all season.
