Wolves' Bakary Sako has revealed he is mulling over offers from the Premier League but is yet to decide on his future.
Rotherham boss Steve Evans will decide the fate of his out-of-contract players in a meeting on Monday.
Scottish defender Reynolds made 14 appearances for the Owls after joining from Motherwell in January 2011 but has been unable to command a regular place in manager Dave Jones' first-team squad.
The 25-year-old joined Aberdeen on loan in January last year and has made 28 appearances for the Scottish side this season.
Kyle signed his first professional deal with Wednesday in July last year but has been unable to force his way into the first-team matchday squad.