The 58-year-old has been on leave from Newcastle United since a club investigation began last year and left his job on Wednesday.
Beardsley has denied the claims, which include one of bullying by midfielder Yasin Ben El-Mhanni.
“We can confirm that the FA is investigating the allegations made against Peter Beardsley during his time at Newcastle United,” an FA spokesman said on Tuesday.
Beardsley was the subject of an investigation in 2003 when he and Kenny Wharton, the then academy director, were accused of bullying.
The case was dismissed.
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