The 27-year-old Briton, who also holds the IBF and IBO titles, had been due to face Wladimir Klitschko in a rematch of their April bout that Joshua won via an 11th round knockout.
But the Ukrainian announced his sudden retirement on Thursday.
“Both parties (Joshua and Ortiz) were duly notified that as of August 3rd, they have 30 days to reach an agreement or the fight will be called to purse bids,” the WBA said in a statement.
Joshua, undefeated in 19 bouts, has also been told he must face IBF mandatory challenger Kubrat Pulev of Bulgaria before Dec. 2 or risk being stripped of that belt.
The 38-year-old Ortiz is also unbeaten, recording 23 knockouts in 27 career wins, and is a former WBA interim world champion.
Former champion Klitschko, who made 23 world title defences during his glittering career, has backed the Briton to lead the next generation of heavyweight fighters.
“My HEART is at PEACE as I pass the torch to @anthonyfjoshua – the next generation. Good luck little bro. I’m proud of you!” the 41-year-old posted on Twitter.