Phillips has signed a short-term deal until the end of the season following his release by Crystal Palace, with whom he won his fourth promotion last season.
He scored the match-winning penalty against Watford in their Sky Bet Championship play-off final at Wembley, but made just four appearances from the bench for the Eagles in the top flight.
The 40-year-old is set to be out of contract again at the end of the season and had claimed that he will hang up his boots this summer after two decades in league football with nine different clubs.
But with Leicester currently leading the Championship by four points the Foxes are well-positioned to seal a return to the Premier League after a decade-long absence, and Phillips may fancy another crack at the the highest level.
"I've been fortunate enough to get promoted four times before and there's a massive incentive for me to get another one," Phillips told the Daily Telegraph.
"I never dreamed I'd be playing in the Premier League at the age of 40 but now I've got another chance to help a team get there, which is amazing.
"The intention is to retire at the end of the season but I've learned to never say never in this game. If we are playing Premier League football next season and I still think I can do a job, who knows what might happen?
"We're in a great position here but there will be so many twists and turns. You can play three games in a week and be in a completely different position."
Phillips has previously won promotion with Sunderland, West Brom and Birmingham.
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