"The manager Craig Levein and I both have copies of the offer and will get together in the morning to go through it. We both want Barry to stay."
Robson has been linked with moves to Celtic, Newcastle United and Burnley, but it appears League One Forest are the first to match Dundee United's valuation of their star midfielder.
Thompson added: "We will do everything in our power to keep him, but sometimes these things are taken out of your hands."