Hoey, who led after the first round alongside Sweden's Sebastian Soderberg after a brilliant 61, carded a three-under 68 in Friday's second round.
Quiros birdied his last four holes for a 63 to go two strokes clear on 14 under par for the tournament.
Soderberg matched Hoey's 68 and the pair are tied on 13 under.
Hoey, who lost his full European Tour card last year, recorded six birdies and three bogeys in his second round at Verdura Golf Club.
Former Masters champion Mike Weir made his first halfway cut since November 2014 after a battling second round of 70.
The Canadian recovered from a triple-bogey on the 18th - his eighth hole of the day - to finish right on the cut mark of five under par.
Weir, who has slumped to 1,907th in the rankings, has struggled for form ever since undergoing elbow surgery in 2011 and announced in July 2015 that he was taking an indefinite leave of absence from golf for family reasons.
Northern Ireland's Michael Hoey lies two shots behind leader Alvaro Quiros of Spain at the halfway point of the Rocco Forte Open in Sicily.