The Brazilians are long-time admirers of the former Stellenbosch FC winger and had previously made enquiries about his availability during the January transfer window as they explored options to strengthen their attacking department.
Sundowns were also monitoring several other targets at the time, including Puso Dithejane, who later signed for Chicago Fire in the MLS, before eventually deciding to bring in Monnapule Saleng from Orlando Pirates.
It is understood that discussions between Sundowns and SV Ried have progressed considerably in recent weeks after an earlier attempt to secure Van Wyk's services failed to gain traction.
At the time, the Austrian club's valuation of the player was believed to be above what Sundowns were prepared to pay, resulting in negotiations cooling off.
However, the public broadcaster understands that there has now been a positive shift in talks between the two clubs, with all parties continuing to work through the finer details of a potential transfer.
While a breakthrough has been achieved, sources have indicated that a number of aspects still need to be finalised before any move can be considered complete.
van Wyk has established himself as an important player at SV Ried since moving to Austria, helping the club secure promotion to the top flight and becoming a regular feature in the side.
Although Ried exercised an option to extend his contract until July 2027, the player remains a subject of interest for Sundowns as they assess their squad ahead of the new season – and the latest discussions suggest he could be leaving.
The reigning African champions have been relatively quiet in the market since lifting the CAF Champions League title earlier this month but the latest developments suggest they remain active behind the scenes.
Whether the negotiations ultimately result in a transfer remains to be seen, however SABC Sport understands that discussions are moving in a positive direction as Sundowns continue their pursuit of the 24-year-old attacker.