The lawsuit comes as USADA is seeking a lifetime ban against Drummond for supplying the joint second fastest man in history with performance-enhancing drugs.
"Mr. Drummond's baseless lawsuit against the US Anti-Doping Agency is an effort to circumvent the mandatory arbitration process established to protect the rights of all clean athletes, coaches and the integrity of competition," USADA spokesperson Annie Skinner told Reuters.
"Under the rules which were approved by athletes, the US Olympic Committee and all US sport federations, Mr. Drummond will have the opportunity to have his case heard by a panel of independent arbitrators, who will ultimately weigh all evidence presented and determine the outcome of the case.
"As in numerous previous cases, we will ask the court to dismiss Mr. Drummond's lawsuit in favor of the well-established arbitration process."
Neither Gay nor his agent responded to requests for comment.
Drummond, a former Olympic sprinter who coached the US relay team at the 2012 London Games, filed a defamation lawsuit on Wednesday against Gay, USADA and USADA chief Travis Tygart.
"Mr. Drummond categorically denies ever having encouraged Tyson Gay, or any other athlete, to use any banned substance," Mark Whitburn, one of Drummond's lawyers, said in a statement emailed to Reuters on Thursday.
"Mr. Drummond has been a vocal and active proponent of clean competition throughout his career ... allegations that Jon Drummond has ever encouraged any athlete to use banned substances are false and defamatory.
"USADA's, Travis Tygart's and Tyson Gay's words and actions are designed to cause great harm to Mr. Drummond, and he has brought this lawsuit in an effort to protect his reputation and demonstrate that he has acted with integrity in his dealings with Tyson Gay and USADA, just as he acted with integrity throughout his career as an athlete and in coaching others."
Gay, the gold medal winner in the 100 and 200 metres and 4x100 metres relay at the Osaka world championships in 2007, was handed a one-year ban earlier this month after testing positive in 2013 for a banned anabolic steroid.
He has returned the silver medal he won with the US 4x100 metres relay team at the 2012 London Olympics but will be eligible to return to competition as early as next month after admitting his offence and co-operating with investigators.
As part of the suspension he accepted, Gay was disqualified from all competitive results since July 15, 2012, the date he first used a product that contained a prohibited steroid.
The start of his ban was backdated to June 23, 2013, the day his doping sample was collected at the USA Outdoor Track & Field Championships and when he voluntarily stopped competing after being notified of his positive test.
Only Jamaican world record holder Usain Bolt has a faster 100 metres time than Gay, whose 2009 clocking of 9.69 seconds was later equalled by Jamaican Olympic silver medallist Yohan Blake in 2012.
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