The Western Mail says McPhail, 33 - who played over 220 games for Cardiff after being signed by Jones in the summer of 2006 - interested the Owls in January and is leaving the Bluebirds under freedom of contract.
"I have loved playing for Cardiff and enjoyed being even a small part of the club's title triumph this season," he said recently.
"I want to play on for a couple of seasons at least. I am fit and ready and, for the first time in six or eight months.
"I am back to where I was three years ago. Getting back to first-team football is important to me."