Taylor, last season's top scorer in the old second division, has been linked with a move to Hillsborough all summer long.
The Owls are set to step up their interest with a confirmed bid for the hitman so he can hopefully join the cub before their pre-season preparations begin in a Ibiza-based tournament.
But a move for Luton's Steve Howard is set to be scrapped now Turner has sealed the deal of Lee Peacock on a two-year contract.
The Owls boss wants a target man and a more mobile striker, and with the capture of the Bristol City star there seems to be no need for Howard now.
Replacing Peacock at Ashton Gate could be Rangers' Owls target Steve MacLean after boss Brian Tinnion and the Ibrox club agreed a fee, although Turner could still be interested in the youngster.
Elsewhere, Lawrie Wilson is set to join Nigel Clough's ambitious Burton Albion.
The son of former player and attempted 'manager' Danny was released last season so he could pursue first-team opportunities away from S6.