Steve Bruce has been widely tipped to succeed Jos Luhukay, who was sacked last Friday, and The Star understands the Owls remain in advanced talks with the former Manchester United defender. Bruce is currently away on a pre-planned family holiday.
But Bullen, who led the Owls to a superb 1-0 triumph at promotion-chasing Middlesbrough, told The Star: "I would think there will be an announcement in the next couple of days. It is not the sort of thing you want dragging on and dragging on.
"I think it needs to be done sooner rather than later so the players know exactly where they stand as well because you don't want people in limbo.
"The sooner it is done the better, in my opinion, especially with a transfer window coming up.
"I don't know where we are at financially. That's not my remit but there is the potential to freshen things up and go from there.
"It would be nice for it to be done from that point of view but I genuinely don't know what is happening."
Adam Reach grabbed his seventh goal of the campaign to wrap up back-to-back Owls wins under Bullen.
"I will just keep going until I'm told different," said Bullen. "The players have been fantastic, they've shown professionalism, discipline and the fight for each other that has got us the two victories.
'They've put in a right shift against one of the most experienced teams in the Championship in Middlesbrough.
'They've battled for everything, covered for each other and I'm delighted for everyone connected to the club."
Wednesday are next in action against West Bromwich Albion on Saturday.
Bullen said: 'This division is brutal. It's relentless. There is not a lot of time for tactics so we have to make the most of the limited time we have."