MacAnthony used his Twitter account to inform supporters of the situation regarding Boyd, who has been subject of recent interest from a number of Championship clubs.
"Can confirm that we have accepted multiple bids for George Boyd," MacAnthony tweeted.
"Down to the player now to agree terms with clubs tomorrow."
Earlier this week, MacAnthony used the social media site to confirm that a deal had been agreed with Crystal Palace for Boyd, but Sky Sports understands that Nottingham Forest are favourites to sign the player.
Boyd, who joined Peterborough from Stevenage for £260,000 in 2007, spent time on loan at the City Ground in 2010, but a permanent deal never arose.