Maresca boasts an impressive reputation and is currently working as Pep Guardiola's number two at the Etihad Stadium.
It's been a blockbuster season for City who secured a precious treble by winning the Premier League, FA Cup and Champions League to become the first English side to achieve the feat since Manchester United in 1999.
But while shining as a deputy, Marescsa could be tempted by the chance to step out on his own.
It could be the second time Guardiola has lost his assistant with Mikel Arteta joining Arsenal in 2019.
Leicester have also not removed Graham Potter from their list of candidates, but the former Chelsea chief is happy to bide his time before returning to the dugout.
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The Foxes are looking for a new boss after suffering relegation from the Premier League last month.
Dean Smith had been in interim charge following Brendan Rodgers' decision to leave Leicester by mutual consent in early April.
Despite his best efforts, the former Aston Villa and Norwich boss couldn't stop the Premier League giants from suffering relegation.
As a result, they'll be preparing for their first season in the Championship since the 2013/14 campaign when they won the title under Nigel Pearson.