It followed a dramatic couple of days at Glanford Park, where manager Ian Baraclough along with assistant Kevin Pressman and first-team coach Steve Parkin were sacked following Tuesday's 3-0 home loss to Preston North End.
Hayes and Williams quit the Iron in the summer when their contracts expired, choosing the comparative riches on offer at Preston and Reading respectively.
The moves have not worked out for either player, with both quickly dropping out of the first-team pictures at their clubs and going out on loan.
Steve Wharton, the Iron chairman, said he had spoken to Hayes about a third spell at Glanford Park.
"I did my best to try and encourage him to come back," he told the Scunthorpe Telegraph, adding that he would not rule out a future return.
The BBC claimed Hayes had agreed to return, but Preston would not sanction a move.
Phil Brown, the Preston manager, has previously said he woud not allow the forward to move to a relegation rival.
A move for Williams was ended when the player, who can play as a left-sided full-back or midfielder, suffered an injury on reserve team duty.
Tottenham Hotspur winger Danny Rose was also a target, but the Premier League club would not allow him to leave while there is the possibility of him being needed in their matchday squad.
The BBC also claim the Leeds United winger Ross McCormack is a target.