Brazil-based web site portaldovaletudo.uol.com.br first reported the bout earlier on Monday.
According to the source, Machida vs. Davis clears the way for current UFC light heavyweight champion Jon Jones to defend his title against Alexander Gustafsson on Aug. 17 in Boston or Sept. 21 in Toronto. The date is contingent on how quickly Jones heals from a foot injury suffered in April during a victory over Chael Sonnen at UFC 159.
Machida, ranked second among light heavyweights by ESPN.com, will look to extend his win streak to three when he faces Davis. He will carry a 19-3 record into the fight.
In his most recent outing, Feb. 23 at UFC 157, Machida secured his position as the top 205-pound contender with a unanimous decision victory over Dan Henderson.
Davis, who ESPN.com ranks sixth among light heavyweights, has a professional MMA record of 11-1. His lone setback came on Jan. 28, 2012, a loss by unanimous decision to Rashad Evans.
Since the loss, Davis has fought three times -- two wins and a no contest.