The Owls have reportedly bid for David Jones.
Jones (front right) in action during pre-season
However, the 31-year-old may find his opportunities limited by the imminent arrival of Steven Defour at Turf Moor, while Aston Villa midfielder Ashley Westwood is also said to be a target for manager Sean Dyche.
Villa's Westwood has been linked with a move to Burnley
Wednesday, who narrowly avoided joining Burnley in this season's top flight, are looking to go the distance this time around and have already added Premier League pair Steven Fletcher and Almen Abdi to their ranks.
Fletcher (number 6) attempts an overhead kick
Jones would be another high quality addition, although the former Manchester United man might yet opt to stay put.
Owls head coach Carlos Carvalhal said earlier this month he is keen to sign four more players this summer, including a centre-back, left-back, midfielder and winger - taking the total number of incomings to nine.
Meanwhile, last season's top scorer Fernando Forestieri looks set to stay put after issuing an apology on social media this morning, following his refusal to play in Saturday's draw at Norwich City.
Forestieri scores Wednesday's winner against Aston Villa