Irvine will be sidelined for at least three months after having surgery on a foot injury suffered when playing for Bundesliga club St. Pauli.
Popovic said Irvine's absence was "certainly a blow" for the Socceroos as their hopes of an automatic ticket to the 2026 finals hang in the balance ahead of a home qualifier against Japan (June 5th) and a trip to face Saudi Arabia (June 10th).
"He played very well for us in the last (international) window and has been doing very well at St. Pauli," Popovic told Australian media.
"It’s a blow, but we have to find a solution. There are solutions.
"We’ve got an eye on the A-League players that are playing, but we’ve got a lot of midfielders playing overseas at the moment, getting regular minutes, so we’re monitoring everyone.
"There’s an opportunity for someone to come in."
Popovic said uncapped Europe-based midfielders Max Balard and Nectarios Triantis could come into consideration in the absence of 78-cap veteran Irvine, who scored in the 2-0 qualifier win over China in Hangzhou in March.
Second in Asia's Group C on 13 points, Australia will qualify directly for the World Cup in North America if they can hold their place.
Japan have already qualified on 20 points, while third-placed Saudi Arabia, three points behind the Socceroos, are also in the hunt for the automatic berth which comes with a top-two finish.
The third and fourth-placed teams will have further chances to qualify in the fourth round, though.
Australia will have a training camp in late-May in Abu Dhabi that will allow staff to assess all the options for the qualifiers.
Popovic said an assistant coach would also run the rule over young Italy-based defender Alessandro Circati as he closes in on a return to action for Serie A side Parma following an ACL injury.
"Paul Okon will be going to visit him in the next few days to have a really close look at where he’s at in terms of his training and to see his level,” Popovic said.
"(Circati) feels he's ready, but we have to consider all factors before selecting him."