Coyle will be unveiled by their Lancashire rivals Bolton once compensation has been agreed.
In the meantime, Burnley coach Steve Davis has been named caretaker manager and will take charge of the team for Saturday's Premier League meeting with Stoke.
Flood said: "I think we would like to have the same recipe again as much a possible and there are choices that we can consider.
"We have just got to meet them and make sure they have got the chemistry, the right feeling for Burnley, and hopefully make a decision within the next two weeks.
"The January window puts extra pressure on everybody. We will be looking for somebody who can make a difference quickly.
"We are very happy with our squad and if we only made one or two additions nobody would complain.
"But we want to give any new manager the opportunity to look slightly beyond that and see what he wants to do.
"It's a challenge. Owen has done a magnificent job for Burnley. I don't think any of us would deny him that."
Flood expects a plenty of applications for the post.
He said: "There are always young, hungry, winning managers who want to do something and make their name.
"I think there will be a lot of interest. That gives us much more choice and hopefully we will get someone with a real ambition for Burnley and the commitment to drive the club forward in the short term.
"We've got to get ourselves up as it is a new chapter in the club's history.
"If we can attract the right guy that might add something to what we've got here, who knows where that might lead."
Burnley travel to Bolton on January 26 with relationships strained between the clubs.
Chairman Barry Kilby Kilby said: "I don't think we are best of pals at the moment. It was an unwelcome approach.
"Owen felt Bolton do have a larger player budget than we have and it was his best way of remaining a Premiership manager, working with a budget of that size.
"It's been a trauma for the football club. None of us wanted Owen to go. It was a shock when all this broke. We are all grown men and know how football works but it was quite emotional when Owen left."