McKay said: "I will look across the whole organisation – the football side, the business side, the engagement side – and we'll make sure we've got the right structure for the next decade.

"But with the experience that we've got with (new manager) Ange (Postecoglou) at the international level and the professional level in Japan and Australia, I'm going to tap into great expertise here to make sure we've got the right football environment."

When asked if Dundee technical director Strachan was coming in as director of football, McKay said: "No. One thing any new chief exec wants to do is to look across the whole organisation. That is a fantastic club with really solid foundations.

"But I want to make my own mark and part of that is looking across how we might want to modernise and to evolve.

"We'll take our time. We'll put the right structures in place to make sure we've got a modern, forward-looking club.

"I'm completely open-minded. I think the suggestion was Gordon is coming in to do a director of football role. That's not the intention.

"Once we've got an idea for what the right kind of structure is, we'll get the right people to populate that."

Meanwhile, Lawwell will continue to represent the club on the board of the European Club Association after retiring from his role at Celtic Park.

"So Peter will certainly finish up at the end of this month with his responsibilities at Celtic Football Club," McKay said.

"We've got another two years to go on the European Club Association, which is a really important role for Scotland and the club to have representation there, so he will stay engaged with that.

"What has been brilliant during the whole transition is that Peter has been fantastic to me. He's achieved so much and has been kind enough to say he will be on the end of the phone for me. So if there's any interesting questions I want to bounce off him he is always going to be there for me and the football club."