The 27-year-old had been due to face Wladimir Klitschko in a rematch, before the Ukrainian retired on Thursday.
The WBA says Joshua and Ortiz have 30 days from 3 August to agree the fight.
Joshua, who beat Klitschko at Wembley in April, has also been told he must face IBF mandatory challenger Kubrat Pulev before 2 December or risk being stripped of his belt.
There had been plans for Joshua to fight Klitschko in Las Vegas on 11 November and Ortiz’s manager, Jay Jimenez, has said his fighter could fill the void.
Jimenez told Boxingscene: “We are next. We have no problem fighting on that date of November 11th in Las Vegas. Our mandatory takes precedent over Pulev’s and they know that.”
Ortiz, 38, has 23 knockouts from 27 wins, while Pulev, 36, has one defeat in his 26 fights, with 13 stoppages.
Joshua holds two of the four major belts, with New Zealand’s Joseph Parker the WBO champion, while American Deontay Wilder has the WBC belt.