The Serb, who will officially take charge on 1 July, has identified the centre of defence and central midfield as two priority areas for improvement.
Phil Jagielka left Bramall Lane earlier this summer and if 24-year-old Bryan was to follow him out the door it would leave the Blades light in a key area, with question marks also remaining on Jack O’Connell’s fitness.
Young Wolves defender Dion Sanderson has been linked with Sheffield United again following a successful loan spell in League One with Sunderland.
Here are the latest transfer deals and rumours from around the Sky Bet Championship.
1. Bramall Lane rumours
United's transfer activity is set to hot up next month when Slaviša Jokanović officially takes charge. Photo: MICHAEL REGAN
2. Leeds hunt Blackburn forward
Reports claim Leeds United could make a move for Blackburn Rovers' 22-year-old forward Ben Brereton following his impressive performances for Chile at the Copa America. Photo: Clive Brunskill
3. Longstaff on the move?
Newcastle United's 21-year-old English midfielder Matty Longstaff is wanted by Norwich City, Middlesbrough and West Brom, as well as Belgian side Anderlecht, Chronicle Live reports. Photo: Catherine Ivill
4. Wilmot leaves Watford
Stoke have announced the signing of defender Ben Wilmot from Watford for an undisclosed fee. Photo: Richard Heathcote