Gorkss has found himself out of favour at Reading in recent weeks and has not featured for Brian McDermott's men since the Premier League defeat to Arsenal in December.
The news has alerted a number of clubs to Gorkss' possible availability now the loan window has opened.
The likes of Blackburn, Leeds and Leicester were all thought to be keen on the Latvia international, but Wolves are hoping to win the race.
Wolves boss Dean Saunders admitted after Saturday's draw with with Leeds that he was hoping to bolster his defensive options with a new signing and it appears he has set his sights on Gorkss.
The 31-year-old is thought to be interested in a move away from Reading in search of regular first-team football.