The Owls are thought to have made a £10m bid for the striker in January and are prepared to up the ante in their quest to land the 29-year-old, who was sold by Leeds United for £11m in July, 2014.
Fulham are understood to be willing to sell but value the Scottish international at £12m.
The Cottagers have rarely looked like mounting a promotion bid in the two seasons since McCormack’s arrival but the prolific striker still netted 23 goals last term and 19 in 2014-15.
Wednesday’s current record transfer fee paid is the £5.7m paid for Paolo Di Canio to Celtic in August, 1997.
The Owls have also been strongly linked with a move for former Sunderland striker Steven Fletcher and are reportedly closing in on the 29-year-old’s signature.
The forward was released by the Black Cats this summer and has attracted interest from a host of clubs including Norwich City.
Fletcher has also been linked with a move to Celtic but the race for his signature looks between Norwich and Wednesday, who have offered the forward a longer contract than the relegated Canaries.
Another name linked with a move to the ambitious Owls is Villarreal defender Bojan Jokic.
The left-back is entering the last year of his contract with ‘The Yellow Submarine’ and spent the second half of last season on loan at Nottingham Forest.
But despite being linked with a whole host of new arrivals, the Owls face a serious battle to keep star centre-back Tom Lees, who continues to attract strong interest from Burnley.
Wednesday’s Championship rivals Leeds had hoped to sign former Barnsley loanee Ashley Fletcher from Manchester United but the 20-year-old forward is on the verge of joining West Ham.
United have also been linked with a move for Gillingham defender John Egan but he is reportedly heading to Brentford.
More likely for Leeds is a move to sign centre-back Kyle Bartley on loan from Swansea City – former club of new Whites head coach Garry Monk.
Seemingly heading out of Elland Road is centre-back Giuseepe Bellusci, who looks set to join Italian club Empoli on loan.
In the Premier, Middlesbrough are chasing Fiorentina striker Khouma Babacar but face competition from free spending Crystal Palace, who have just landed winger Andros Townsend from Newcastle United for £13m.
Babacar, 23, is likely to command a price fee of around 15million euros.
Boro are also interested in Newcastle goalkeeper Tim Krul.
Barnsley have signed West Ham striker Elliott Lee and the Tykes insist that key trio Alfie Mawson, Conor Hourihane and Sam Winnall are not for sale.
The Reds are also still interested in Walsall striker Tom Bradshaw and could return with a new bid in excess of £350,000.
In League One, Sheffield United striker Che Adams is reportedly attracting interest from one unnamed club in the Premier League, as well as Championship outfits Huddersfield Town and Wigan Athletic.
Bradford City, meanwhile, are all set to sign Shrewsbury Town captain Nathaniel Knight-Percival.
Southend, Bury and Gillingham were all interested in the 29-year-old who is set to join the Bantams on a two-year-deal.