Jackett's five-and-a-half-year spell with the club came to an end on Tuesday when he stepped down from his position.
The bookmakers have Owen Coyle and Bournemouth manager Eddie Howe among the early favourites for the position, but Ambler revealed that the board have yet to identify their main target.
He told Sky Sports News: "We'll take our time. I know everyone will be clamouring for a list but there is no list at the moment. We're just sifting through applicants.
"The squad the new manager will inherit is a decent one and we know where we need to strengthen.
"Kenny Jackett left the club in a much better state than when he joined it. We need to make sure that five-and-a-half years of stability is built on.
"We are an ambitious club and we will take our time to get the appointment right."