Clarke was made available for a move at the start of the summer, after United secured promotion to the Premier League, while Duffy’s name was circulated more recently after he irked boss Wilder by asking for a new contract.
The United manager insisted he would not be "dictated to" by either the player or his agent and Duffy’s future at Bramall Lane appeared in doubt when he wasn't allocated a squad number for the upcoming season.
And, at his press conference this morning, Wilder said: “There are a couple of bits of business that could happen with outgoings.
“There are a couple of bits of interest in Mark, and Leon as well.
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“They’re both established Championship players now, and I wouldn’t be surprised if both of those went by the close of play.”
The deadline for Premier League and Championship clubs is 5pm this evening.
Wilder also expects Ben Heneghan and Jake Wright to depart, although clubs in Leagues One and Two have until September 2 to complete their business.