Youth academy head Eddie May, with the support of Grant Murray, has taken charge of three matches. The former Falkirk boss has been pencilled in to host a media conference on Friday to preview Saturday's William Hill Scottish Cup fifth-round visit of Raith Rovers.

Dempster told Hibs TV: "The search is well under way. We have had a lot of interest in the post and we have been away for the last few days having some conversations.

"We have been on the road, we have been having conversations, and there's some more to be had. Obviously, there are a few games in between that we need to focus on as well.

"But we're not rushing this process and that's the beauty of having great people in the background.

"When you need a bit of time and space to make good decisions, you have some fantastic people there who can take that load and pressure.

"And that's what we have in Grant and Eddie who have been able to take the responsibility for the first team over the last week or so. I'm really grateful to them because it's a tough ask but they have taken on that challenge and done it brilliantly."

Dempster stressed the club would not be adding to the statement which confirmed the departure of Lennon and assistant Garry Parker by "mutual consent" several days after reports emerged that the head coach had been suspended.

"I understand supporters want to know – there is an interest and it's their club," she said.

"But I have to say that there's been a joint statement that's been agreed by all parties and we are really not saying anything beyond that.

"There's been lots of speculation about what happened. One, I can tell you that we haven't been engaging in any media briefings. In fact, we have been getting some complaints from our media colleagues because we have not been, and I'm certain that Neil and Garry haven't been either.

"And I guess it follows then that what you're reading in perhaps the press and hearing on the radio, some of it is, most of it is, speculation."

Dempster refuted rumours she or head of football operations George Craig had been recruiting players on their own and insisted the head coach has had, and will have, the final say.

The former Motherwell chief executive added: "I've read a lot of absolute rubbish about us being in turmoil and it being a shambles, blah, blah, blah. It's totally and utterly untrue, it's just complete and utter drama.

"When events come towards you, you have the benefit of great people, good structure, being able to support you to help you get through periods of difficulty and opportunity. "

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