The 26-year-old midfielder who has made over 350 appearances for the Cheshire club rejected the chance of a new deal at Gresty Road to seek a new challenge elsewhere.
Wolves and Leicester City have been linked with the midfielder too although it now appears that The Owls have won the chase for his signature.
Paul Sturrock has been chasing a new signing before he jets of on holiday this week to join new additions Wade Small and Lunt's former Alex teammate Madjid Bougharra.
Lunt turned down the prospect of a testimonial at Crewe to look for another club despite a very successful time with Dario Gradi and the playmaker is set to sign a deal very soon.