The Dutchman impressed during his recent stint as interim Manchester United boss and he could be in line for a swift return to the Premier League as Foxes executives are said to believe he could be the right man to take over from recently-sacked Steve Cooper.
According to The Sun, the club are believed to be sounding out the 48-year-old former striker over a potential move, but are also considering Graham Potter.
The former Brighton and Chelsea manager has been out of work for over a year but sources told the outlet he could be tempted back into club management with the vacant Leicester job.
Meanwhile, Ruud - who turned down a job at Burnley - is also said to be wanted by Hamburg.
He impressed with his four-game stint in charge at Manchester United, winning three games and drawing once, but new boss Ruben Amorim was keen to bring in his own team.
On his departure, Ruud shared a heartfelt goodbye to fans.
He wrote on Instagram: “To everyone at Manchester United, in particular the backroom staff, the players and the fans.
"I want to thank you from the bottom of my heart for your incredible efforts and support.
“It has been a privilege and honour to represent the club as a player, coach and manager.
"And I will always cherish the memories we have shared together.
“Manchester United will always have a special place in my heart.
"And I hope there are many more glory days at Old Trafford very soon – not only because I want the club to do well, but because you all deserve it!
"All the best and take care, Ruud.”