The manager's two-and-a-half year tenure with Celtic ended last week when he opted to join the Foxes to replace Claude Puel.
The Northern Irishman signed a contract with the Premier League club until June 2022 after winning back-to-back trebles with Celtic while putting the club on track for another trophy-filled season this campaign.
With Rodgers now officially with Leicester, police were called to a property in Glasgow early on Wednesday morning for an incident at the manager's Scottish residence.
A Police Scotland spokeswoman said: "At around 01:55 on Wednesday 6 March, police received a report of a break-in at a property in Bearsden.
"No one was injured in the incident but a number of items were stolen from the property."
Following his exit, a banner was unveiled at Celtic's next match against Hearts that read: "You traded immortality for mediocrity. Never a Celt. Always a fraud."
In addition, video emerged on social media in the aftermath showing fans allegedly singing distasteful chants about Rodgers
Rodgers himself responded to those responses, reiterating to supporters that he is "one of you" who worked as hard as he could to leave the club in a better position than he found it.
The manager's first game in charge of Leicester proved to be a 2-1 defeat away to Watford with Andre Gray's stunning late winner securing all three points for the hosts.
As a result, the Foxes currently sit 11th in the Premier League, two points behind 10th-placed Everton and one point ahead of 12th-placed Bournemouth.
Leicester will return to the pitch against struggling Fulham on Saturday for Rodgers' second match in charge of the club