QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
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.