The forward has been repeatedly linked with a move away from London Road this month and Crystal Palace had a bid accepted earlier this week.
However, a number of clubs, including Nottingham Forest, are now believed to be interested in securing the 27-year-old's services.
"Can confirm that we have accepted multiple bids for George Boyd," MacAnthony posted on Twitter on Wednesday.
"Down to the player now to agree terms with clubs tomorrow."
Peterborough are currently bottom of the Championship.