Martin O'Neill says he can see shades of the Nottingham Forest side that became English and European champions in the 1970s in the current Foxes team.
Leicester, bottom of the Premier League a year ago, are five points clear at the top with seven games to go.
O'Neill played for Brian Clough's Forest when they won the top-flight title in 1978, a year after promotion.
"I see a lot of similarities," he said in a BBC Radio 5 live special.
"There are players I can identify with who are similar in roles they are playing for each side - Riyad Mahrez is a very creative player a bit like John Robertson, your outfield genius, Jamie Vardy looks like Tony Woodcock.
"They are similar with the two players at the back, with Larry Lloyd and Kenny Burns, you could go right through the side and see similarities.
"It is remarkable in this day and age - when big clubs with a lot of money to spend are ruling the roost - for Leicester to come and win this championship would be an almighty achievement."
Republic of Ireland boss O'Neill, who managed Leicester for five years from 1995, was speaking on 'Leicester: The Impossible Team', a 5 live Sport Special to be broadcast on Wednesday.
The 64-year-old was an integral part of the Forest squad that followed up their league title win with back-to-back European Cup victories.
Forest's achievements during that period are largely considered one of football's greatest success stories, and O'Neill believes Leicester City winning the title would be comparable.
"Without question there is romance about the story - people are talking about it all over Europe," he added. "I was in France recently for a Uefa meeting and it was the talk of the evening, people are really taking note.
"It is a great story and if they do it, it would be the story of the century."
'Foxes title would outshine Forest's achievements'