But Mueller is looking forward to working with the former Belgium No.2 and feels that the unpredictable nature of football means unexpected things can happen without warning.
“I don’t think my role will change much. I think I am going to continue to focus on what I can control,” he said when asked about the managerial merry-go-round.
“You never know what can happen in football, but I am really excited to work with Shaun, I have heard amazing things about him as well.
“So I’m really looking forward to what he can bring to the team as well.
“We kind of had the Chicago connection because he had been there and I am from Chicago as well.
“We had a laugh about that. I think he only spent a few months there playing with the Chicago Fire but he said the city was lovely.
"We spoke about the city and the States in general and how far Major League Soccer has come. That was a good chat and a good way to break the ice.
“I’ve heard he was a great player and knowing he was a wide player I think he can be a big help to me.”
Mueller believes the similarity between his role and the one fulfilled by his manager during his playing days can be hugely beneficial.
“I was actually watching Sky Sports yesterday and there was an old Celtic-Rangers game on from 2009 and he featured in it, so I got to see a bit of film work from his playing days. That was a pretty funny moment.
“So yeah, I’m really looking forward to working with him. Even with our playing styles, he was a bit shorter like me and kind of crafty on the ball, good agility and had the ability to create things, take people on one versus one.
“So I am really looking forward to working with him and seeing what I can pull into my game.”