The Great Dane is understood to want a bigger challenge, and is now waiting to see if Celtic follow up their initial approach.
The man who was sacked by Swansea in February - along with his assistant, former Hoops midfielder Morten Wieghorst - has indicated the Danish duo would give serious consideration to succeeding Neil Lennon at Parkhead.
The latest twist came hours after Scott Brown warned that whoever is appointed Celtic manager will have big boots to fill following Lennon's departure.
But the Hoops skipper is confident the legacy the Irishman has left, in the shape of the stability of the club and the strength of the squad, will stand the new Bhoy in good stead.
It's a much more attractive situation than the one rookie Lennon inherited when he stepped into the breach in the wake of Tony Mowbray's sacking in 2010. Back then, the team were in a slump, and major surgery on the under-performing squad was immediately required.
Today, Brown is positive it is a much healthier scenario, thanks to the values Lennon has put at the heart of the club, and is ready to get to work under whoever is selected to take up the reins.
He said: "The squad Neil has brought in has been great. He has a core of players who have stuck together, who fought for him, and that played for him. It has been enjoyment all the way down the line, and that is what he has instilled in us."
The onus is on Brown as longest-serving player and captain to help make the transition as seamless as possible.
This is the third managerial change he has seen in his seven years at the club. But, of the responsibility he insisted: "It's not just on me. I might be captain, but there are a lot of good players in our dressing room willing to talk and willing to give a lot for the club.
"The gaffer (Lennon) imposed that on us, and we will continue this. It will be hard, though, because we know what it is like to be in the qualifying stages for the Champions League."
With the opening games the Champions League Qualifers in July, it promises to be a baptism of fire for the new manager.
And it could be someone who is stepping into this season-defining series of games without any prior experience of the unique pressures involved.
But, Brown has some words of reassurance for whoever that man may be.
He said: "We have been there for the last two or three years. It has been hard, but we have managed to get through, and know what it feels like to qualify for the Group Stages in
Europe. We have got to take that into the games and take a lot of responsibility onto ourselves."
Brown is closely monitoring the names in the frame, and can understand why the competition to get the gig is so strong.
"It's a great job for whoever comes in," he said. "It's a huge club and the supporters are fantastic.
"So, whoever comes in, they will love their time here and enjoy every single minute."
Brown will take his mind off developments at Parkhead tonight as he leads out Scotoand against Efe Ambrose's World-Cup-bound Nigeria side at Craven Cottage.
He is treating this game as much more than an end-of-season friendly as it is the final prep match before the Euro 2016 qualifiers.
Brown said: "We are on a good run and want to keep that going. We know it's going to a hard game because Nigeria are heading to the World Cup and have been together for the last 10-12 days.
"But, our lads have looked after themselves since the end of the club season and are looking fantastic in training.
"At this stage of our preparations for the qualifiers, we don't want to lose the momentum we have built up."