The 24-year-old joined Peterborough on an 18-month deal in March, but MacAnthony has now confirmed the club has offered the striker a new four-year contract.
“We exercised an option on his contract recently, so we’ve got 18 months on Paul,” said MacAnthony.
“I have personally offered Paul a very good contract for four years. We think it will give him a chance to grow.
“Paul Taylor could become anything.
“I think he’s been handled with kid gloves purposefully by the management team, they know how good he can be. When he gets a run of games, he will be explosive.”