Dean returned from suspension as the Bees beat AFC Wimbledon in the League Cup on Tuesday, but saw Nico Yennaris handed the armband instead.
The 26-year-old is out of contract at the end of the current campaign and has yet to accept Brentford's offer of fresh terms, with Wednesday circling according to Get West London.
Brentford's Harlee Dean (left)
Bees boss Dean Smith - a former Owls captain - told the newspaper: "I had a chat with Harlee when we started pre-season. At the moment he's in a bit of limbo with contract negotiations.
"With that going on it's right that someone else carries the armband. He's behind that and accepts that well."
Wednesday remain on the lookout for at least one new central defender after Johan Djourou snubbed a move to Hillsborough in favour of joining Turkish side Antalyaspor.
But according to Smith, Carlos Carvalhal's side have yet to act on their alleged interest in Dean.
"I can tell you we've had no bids from anybody for any players," he added, via Get West London. "There's only speculation that is going around.
"On the first day of pre-season I sat down with Harlee and asked him where he was. His representatives have been in talks with the club but I'm sure his representatives are pitching him around to other clubs as well.
Brentford boss Dean Smith
"He's fully committed to the cause which is great for me. I've got a really good relationship with Harlee and that will continue."
Wednesday are close to over-stepping the Football League's financial fair play boundaries, and have made free agent George Boyd their only summer recruit so far.
But with only two recognised centre-backs currently at their disposal, the Owls are expected to return to market before the end-of-month transfer deadline.
Could Sheffield Wednesday sign Brentford's Harlee Dean?