Clarke has been a key figure for Preston since his 2013 arrival from Huddersfield Town, helping the Lilywhites out of League One and into the Championship's top half.
Simon Grayson's side have endured a tough start to their second season back in the second tier, however, and it could be about to get worse should Wednesday and Blackburn pursue their interest in the 28-year-old centre-back.
The Owls are desperately short of options in that department, with captain Glenn Loovens missing the start of the new season and Tom Lees joining him on the sidelines.
Clarke was part of a Preston defence which conceded 45 goals in last season's Championship, the same amount as Wednesday and fewest of any club outside the top six.
However, the Yorkshireman is out of contract next summer, leaving the Lilywhites vulnerable to offers.