It is alleged Moore has committed multiple breaches of FA Rule E8 (b), which relates to gambling on competitions in which one is involved or has an influence upon during the season in question.
Tranmere suspended the 61-year-old last month pending the conclusion of the FA's investigations, and have declined to comment on the latest development.
Moore has until April 8 to respond to the charges.
Newcastle United midfielder Dan Gosling was fined £30,000 for breaches of the same rule last month, while Andros Townsend and Cameron Jerome have also been dealt punishments for similar offences.
The incidents prompted FA chairman Greg Dyke to reveal that the governing body was considering adopting a blanket ban on footballers betting on the sport - a system already in use in Scotland.
And, speaking to Perform last month, William Hill director of security Bill South said: "The FA are obviously now starting to think about going along the lines of a blanket ban for those people that participate in football.
"There have been a number of cases recently, but I think what that's doing is it's actually highlighting the issue, which is probably what's prompted the FA to start talking about it openly in relation to stopping their people from betting on football."
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