The Championship new boys had made a couple of bids earlier for the Nottingham born striker, who joined City from Southampton, a year ago.
The bids which were more add-ons than hard cash were rejected by the City board and it looks likely that Forest will need to put some serious hard cash on the table if they are to land the scorer of City's goal in last week's friendly against FC Brasov.
Leon Best in action
Chris Coleman rates Best highly and told BBC Coventry & Warwickshire: "He has got so much ability and Leon is certainly not someone that we are looking to sell. "We are looking to build a team with good players. Leon certainly fits into that, he has looked excellent in pre-season."