Maloney, currently preparing for the rescheduled Euro 2021 as the assistant manager to Roberto Martinez with the Belgian national side, has been touted as a possible candidate for the vacancy at the Parkhead club.
Highly regarded in coaching circles, the 38-year-old has emerged as a popular choice among Celtic fans, either as the manager in his own right or as Martinez number two, with the Spaniard also among the bookies frontrunners for the vacancy.
Maloney spent 10 years as a player at Celtic across two spells and coached the U20s before leaving to take up his role with Belgium, where he has worked with stars such as Kevin de Bruyne and Romelu Lukaku and helped secure top spot in the Fifa world rankings.
However, the former Scotland international refused to comment on whether he would accept an approach from Celtic.
Speaking on BBC Sportscene, Maloney responded: "It's an impossible question for me to answer.
"I have to show respect to the federation that have put massive faith in me.
"But from a sporting point of view, I really hope Celtic, whatever decision they make, they make it quickly, because these decisions have to be made.
"They can definitely fight for the title again next year and the big thing they have to do is get that connection with the support again because if that's not there, then they're not going to be able to fight."