Beardsley, who coached Newcastle’s Under-23 side, abandoned the club about 6 March. He had been on leave as a golf analysis began last year.
The ex-Newcastle and England forward has”categorically denied” the asserts.
Beardsley faced multiple ailments, including one of bullying by 22-year-old midfielder Yasin Ben El-Mhanni.
A spokesman for English football’s governing body told BBC Sport:”We can make sure the FA is exploring the allegations made against Peter Beardsley throughout his period in Newcastle United.”
Anti-discrimination charity Kick out it has expressed concern that the Premier League club have not outlined the reasons for 58-year-old Beardsley’s departure.
Back in 2003, Beardsley and academy manager Kenny Wharton faced a premier-league investigation over allegations of bullying made by youth players James Beaumont and Ross Gardner however, the case was dismissed.
Beardsley made 326 looks for the Magpies as an individual player.