The Owls have already rejected two bids from Millwall - one believed to be in the region of £1 million - earlier this summer.
Windass has had surgery on a hamstring injury he suffered in pre-season and will spend the opening weeks of their League One campaign on the sidelines.
Sheffield Wednesday kicked off their season with a 0-0 stalemate against Charlton Athletic at the weekend.
We have gathered the best of League One’s rumours below...
1. Steve Cotterill hints at Shrewsbury midfielder exit
Steve Cotterill has hinted that midfielder Ollie Norburn may leave the club this summer. Cotterill has stripped Norburn of his captaincy and claimed the 28-year-old was well behind his team-mates’ fitness levels. (Shropshire Star) Photo: Naomi Baker
2. Doncaster Rovers in talks with unnamed Premier League player
Doncaster Rovers are said to be in talks with an unnamed attack-minded player from a Premier League club over a loan move. The player is reportedly a long-term target of Rovers and can play in a variety of positions. (Doncaster Free Press) Photo: Lewis Storey
3. Swansea City closing in on deal for Ipswich Town captain
Swansea City are negotiating a deal for Ipswich Town’s Flynn Downes after they accepted an offer in principle over the weekend. The Swans are looking to the 22-year-old to replace Matt Grimes. (Swansea Independent) Photo: Pete Norton
4. Sheffield United set sights on Crewe winger
Sheffield United are reportedly keen on signing Crewe Alexandra’s Charlie Kirk. The Blades could land the 23-year-old for around £500k. (The Sun) Photo: Lewis Storey