West Brom have "faced setbacks" in their search for a new boss but appointing a head coach with "quality" is far more important than rushing into a decision, says chief executive Xu Ke.
Baggies sporting and technical director Luke Dowling left by mutual consent on Monday, with the club's protracted search for a new head coach ongoing.
Dowling and Xu had been leading the hunt for Sam Allardyce's successor.
But owner Guochuan Lai had vetoed the board's first choice, Chris Wilder.
Subsequent frontrunner David Wagner took a job in Switzerland, while former Albion player and coach Michael Appleton has reportedly withdrawn from the race to focus on his project as Lincoln City manager.
Xu thanked the fans for their "patience during a frustrating period" in a statement on the club website.
'A healthy budget in order to succeed'
"I understand having a vacant head coach position can lead to uncertainty, but this is not a simple search, and we must appoint the correct person," he added.
"Our aim remains the same - to earn promotion back to the Premier League as soon as possible. We will have a healthy budget in order to succeed in the Championship and, with the right person as our head coach, I believe we will have a strong opportunity to be promoted.
"While we have not yet formally offered the job to any candidate, it is fair to state we have faced setbacks and, with that in mind, I do not think it is wise to set a precise deadline by which an appointment will be made.
"The quality of our next head coach is of far greater importance than how soon they can be appointed."
Xu said Dowling's departure gave the club a chance to "reassess how our football operation functions".
"I will provide a further update on this subject in due course," Xu said.
"I would like to thank Luke for his work behind the scenes at The Hawthorns during his three years with us."
Lai to have final say in manager search - analysis
BBC Sport's Simon Stone
With less than two weeks to the start of pre-season training, West Brom now find themselves without both a manager and a technical director and a growing sense of foreboding amongst their fans about the future direction of the club.
Chief executive Xu Ke has said he will take his time making a managerial appointment and the exit of Luke Dowling means he can go down the old-fashioned manager route now in addition to the head coach template that had been in position.
That does not mean a return to first choice Chris Wilder. BBC Sport has been told owner Guochuan Lai vetoed Wilder's appointment after being unwilling to appoint someone who had been critical of his previous owner at Sheffield United.
However, whilst they are working to a reduced budget following relegation from the Premier League, it is understood, within reason, West Brom would be willing to pay compensation if their eventual target turned out to be in a job.
Given how events have unfolded since Sam Allardyce announced he would be leaving The Hawthorns on 19 May, the need to make the right decision is paramount. And for all the soothing words about time, the clock is ticking.
Xu will lead the search. Lai, clearly, will have the final say. Whilst that process is taking place, other staff members have been delegated to put together a pre-season programme which, so far, features a single game, at Watford, on 24 July - two weeks before the Baggies' Championship campaign is due to start.