The Sun said that Taylor, who has been in the role since 1981, had gambled £4m in 2000 bets over two-and-half years, and owed a now-defunct telephone betting firm just over £100,000.
"The Management Committee are aware of the recent press allegations regarding Gordon Taylor," the PFA said in a statement on its website.
"Whilst this is a private matter for Gordon, he has informed us that this dispute has been in the hands of lawyers for some time. For that reason, it would be inappropriate for us to comment specifically. We have discussed this with him and he has our full support.
"We recognise that gambling is part of our culture and part of football and it is for that reason that the PFA remains committed to continue in its work to raise awareness levels and educate."
The 68-year-old Taylor has recently spoken about the "social responsibility" of his members and called for zero tolerance towards gambling, as well as highlighting its dangers for players.
The PFA recently fined and suspended Tottenham Hotspur's Andros Townsend for breaching betting regulations. Stoke City's Cameron Jerome was also fined £50,000 for admitting a breach of the rules.
Managing director of League Two side Accrington Stanley Robert Heys was suspended from the game for 21 months after admitting 735 breaches of betting rules.
The PFA was formed in 1907 and is the world's longest established professional sportsperson's union.
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