"Our managerial appointment must be the start of a new beginning and we will be taking the utmost care to make sure we have the right man," said Hulley.
Reid's competition for the post includes Leicesters director of football Dave Bassett, former Ipswich boss George Burley, and one-time Owls keeper and now Hartlepool boss Chris Turner.
Burley has already been interviewed, while Turner has taken Hartlepool to the top of the Division Three table.
Wednesday are hoping to name their new boss before their next game against Norwich City at Carrow Road on Saturday.