MacAnthony also revealed that Forest, who beat Peterborough 2-1 at the City Ground on Saturday, are not the only one of Posh's npower Championship rivals to express an interest in Boyd, with Crystal Palace and Millwall also making enquiries about the 27-year-old along with Premier League club Reading.
He said on Twitter: "In answer to all the queries on Boydy, we have rejected a formal written offer from NF which I felt was derisory.
"The other clubs who have enquiries for George in the last 10 days are Reading, Millwall and Crystal Palace, with their managers/dof's (director's of football) speaking directly to us about him."
MacAnthony will not offload Boyd, who had a loan spell at Forest during the second half of the 2009/10 season, on the cheap despite the player being out of contract in the summer.
The Posh owner would rather lose Boyd for nothing at the end of the campaign, hopefully having helped the club maintain their Championship status.
He added: "As it stands right now, unless it's a proper offer for player of his calibre I would rather he see out the rest of his contract with us."