Oldham's owner Abdallah Lemsagam says he is looking at selling the club after receiving written threats, including being sent bullets in the post.
A handwritten letter was sent to Boundary Park and was signed by 'The Anonymous Group'.
Lemsagam's brother Mohamed, who acts as Oldham's sporting director, also received a personal letter threatening him and his family, along with a bullet sent in the post.
A statement released by Greater Manchester Police said: "We are aware of a situation involving a report of malicious communications at Oldham Athletic Football Club.
"Our investigation is in its very early stages and our enquiries are ongoing."
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Abdallah told Sky Sports News : "It's not about football anymore."
The former football agent, who completed a takeover of the Latics in 2018, confirmed that he had begun early talks with two interested parties.
In a lengthy statement posted on Oldham's website, Lemsagam said: "Since I purchased the club four years ago I have invested money and time trying to clean the club of all of its historic issues. There were very many.
"Although that work goes on behind the scenes, it is now almost complete with only the North Stand issue to resolve. I have invested in the litigation process and that may need a court to rule on it to get justice for the club and recover what rightfully belongs to it.
"On the playing side, things have not gone how I wanted in the last four years, to say the least. I made mistakes and I won't make excuses - we are where we are.
"In the short term, I am now focused on improving the squad to fight the relegation battle we are now in.
"In the medium term, I can see that my ownership has caused unrest within the club and the fans. I want the best for the club and I think the best for the club is that it is now passed on to new owners. My team is speaking to certain credible bidders and I am happy to speak to others.
"I would ask that every section of the fanbase gets behind the team, whatever you think about me it is in everyone's interests that our great club wins this battle."
Lemsagam's reign has been dogged by controversy, leading to a seemingly untenable relationship with a large section of the club's fans.
Earlier this season thousands of fans protested outside Boundary Park with a mock coffin, whilst pitch invasions have also occurred on numerous matchdays.
In December the club attempted to ban three fans for 'promoting dislike' of the owner. After initially demanding an apology, Lemsagam reversed the decision, following backlash.
The club were relegated into the fourth tier in his first season as owner and have since posted three bottom half finishes in League Two.
This season has been a bigger struggle and they currently prop up League Two and are four points adrift of safety.
Manager Keith Curle was dismissed in November with former youth team boss Selim Benachour stepping up since.
The team's last league victory was back on November 20. In addition, this weekend's proposed visit of Leyton Orient has been postponed due to injuries and positive Covid-19 cases within the Latics' camp.