The National League club revealed on Wednesday Deadpool star Reynolds and fellow actor Rob McElhenney were interested in investing.
The move has been overwhelmingly backed by the Wrexham Supporters Trust, who have owned the club since 2011.
"Talks with the proposed bidders will now continue and we are in a position to confirm the two people interested in investing in Wrexham AFC," said a statement from the club, who play in the fifth tier of the English game.
"In due course, Mr McElhenney and Mr Reynolds will put forward their vision for Wrexham AFC and proposal for members to vote on at a second special general meeting," it added.
Drakeford talked up the club during a TV interview on Good Morning Britain, saying he would welcome Reynolds to Wales.
"There are huge benefits to being part of Wrexham Football Club, the oldest football club in Wales with a fantastic fan base, utterly loyal, owning the club itself," he said
"This is a Hollywood actor. If he can play centre-forward, I'm sure he would be welcome."
Afterwards, he tweeted: "It's not every day you get asked about @Wrexham_AFC on national TV. I can neither confirm nor deny the rumours, but I welcome the excitement around some Hollywood glitz coming to the racecourse ground - I hear @VancityReynolds has an eye for goal!"