Blades manager David Weir confirmed McDonald had been allowed to speak with Wolves, but insisted he did not want the 24-year-old Scot to leave Bramall Lane.
A club statement read: "Sheffield United is aware of the transfer speculation with regards to Kevin McDonald (on Friday).
"The club wish to stress it has no desire to lose Kevin. However, Wolverhampton Wanderers have triggered a clause in Kevin's contract by meeting the fee and, subsequently, the player has been allowed to speak to club.
"Additionally, there is a verbal agreement between David Weir and Kevin McDonald that the player will speak to Sheffield United before committing his future elsewhere."
Weir said: "Obviously we are aware of the situation with Kevin and we couldn't really stop that.
"It would be a blow to lose him; you can't get away from that, but we'll see what develops, there's still a bit of water to go under the bridge."
McDonald made over 50 appearances for Burnley following a £500,000 deal that took him from first club Dundee in 2008 and joined the Blades on a free transfer following his release from Turf Moor in 2011.
He has been a regular during his two seasons at Bramall Lane under previous manager Danny Wilson and was expected to play a key role in Weir's first season in charge as the Blades target promotion from Sky Bet League One at the third attempt.