The pair, who have collectively won seven DP World Tour events, have both confirmed their entry, with neither player having full status on the DP World Tour or Challenge Tour for the 2024 season.
Fernandez-Castano, 43, hasn't won on the DP World Tour since 2013, while Quiros, 40, has also been out of the winner's circle for some time, having not tasted victory since 2017.
The full field for LIV's equivalent of Q-School has yet to be announced; however, an announcement is expected to be made once the final two second-stage sites for PGA Tour Q-School finish on Friday.
While speculation surrounding the field for LIV's inaugural qualifying event has been rife in recent weeks, Monday Q info reported last week that the field would include a host of high-profile names, including a former major winner, a multiple-time PGA Tour champion and a top 100 ranked player.
LIV's promotions event will run over three days set over two stages, with the top three finishers receiving a lucrative spot in the Saudi-backed league for the 2024 season. Players who finish from 4th to 10th will also qualify for next year's International Series on the Asian Tour, which will, in turn, provide a pathway to qualify for LIV.
Despite penalising players for joining LIV in the past, the PGA Tour has stated that they would not be dishing out fines to players for competing in the qualification event if they were granted a media release.
For those hoping to compete, a media release must have been granted 45 days before the event.
Players from the DP World Tour have also been asked to submit requests to play in the qualifying Tournament due to the fact that it clashes with the Alfred Dunhill Championship in South Africa.