However, Gannon, after taking his time mulling over the offer, has rejected MacAnthony's offer, citing family reasons as one of the factors in his final decision.
Although Peterborough's form had improved of late, three consecutive Championship defeats - including Tuesday's 4-0 loss at Scunthorpe - means they remain strong favourites for the drop.
"Having given the matter considerable thought, I have decided not to accept the football club's offer of a contract to be the manager of Peterborough United for the coming seasons," Gannon confirmed on the club's official website.
"I have enjoyed myself immensely over the last few months and would like to thank the chairman and Barry for the privilege of working in the Championship with Posh.
"As you are aware, I am not driven by personal financial gain or a mechanical professional drive. I have become a devoted family man over the last few years and the separation from the family over the last season has created a big void in my personal happiness and contentment.
"Given that my partner is now pregnant and expecting our second baby in July, the need for their stability, security and happiness becomes increasingly important to me. I always promised myself, on behalf of my family, that I would always seek to strike a balance in my professional and personal life."
Despite Gannon's long-term decision on his future, he insists he remains committed to helping Posh retain their Championship status between now and the end of the season.
"I still have an important job to do for the remainder of the season in showing that the players and club are much more capable than what has been previously shown, and that we are determined to use this period to prepare successfully for the new season," he continued.
"There is valuable work to be done over the coming months and we want to gain, collect and learn from these experiences to ensure the successful return to Championship Football for Peterborough United."
MacAnthony accepts Gannon's reasoning behind his decision and believes the improvement under his stewardship gives him hope for the future.
"Whilst I am obviously disappointed with the decision, I have to say that Jim's brief tenure has shown what can be achieved in a relatively short period of time," said MacAnthony.
"I completely understand and respect his reasoning and obviously wish him and his family all the best in his home and professional life as we move forward.
"Planning for the new season is obviously a major priority and we will work hard to make sure we are ready to make the right appointment to carry on the good work that has been undertaken over the last few months.
"There are still seven matches remaining and while there are still important points to play for, the players and manager will give their all for this football club."
Peterborough v Bristol City. Click here to bet.
Source: Team Talk
Source: Team Talk