Wednesday, who parted company with head coach Carlos Carvalhal on Christmas Eve, were said to be considering a move for Karanka even before then [the Sun].
And the former Middlesbrough boss's comments suggest he would at least consider an approach from the Owls - should one materialise.
"I want to develop a good project," said Karanka, who lives less than 50 miles from Hillsborough in Harrogate, North Yorkshire. "I'd like to stay in England. My family is really comfortable here."
Karanka, who took over Middlesbrough when they were 16th in the Championship - two places lower than Wednesday are now, and led them to fourth in his first full season at the Riverside, but lost in the play-off final.
The 44-year-old went one better the following campaign, however, taking Boro up in second, but he left by mutual consent with the Teessiders battling relegation from the Premier League earlier this year.
Wednesday trio Adam Reach, Jordan Rhodes and Jacob Butterfield played under Karanka at the Riverside, but were all moved on eventually.
Should Sheffield Wednesday move for Karanka?