Maresca has long been the clear favourite to take over as Manchester City head coach following Pep Guardiola's departure from the club this summer, but the move has been complicated by a dispute with his former employer, Chelsea.
Chelsea believe Maresca breached his contract and are demanding financial compensation from City before agreeing to release him.
The London club say they have evidence that the Italian held talks with a Premier League rival while he was still Chelsea's manager last season.
The Guardian reports, however, that the two clubs are now close to finding a resolution that all parties can accept.
According to the newspaper, a settlement in excess of £10m appears to be the likely outcome of the negotiations, clearing the way for Maresca to formally succeed Guardiola in the City dugout.
The dispute has rumbled on for weeks despite Maresca's move to Manchester City being widely reported as a formality once Guardiola's exit was confirmed. Chelsea's insistence on compensation reflects a wider pattern in English football of clubs seeking financial redress when a manager leaves under circumstances they consider a breach of contract, even when the coach in question is moving to a significantly bigger role elsewhere.
Once the compensation issue is resolved, Maresca will be free to begin work on rebuilding a City squad that finished the season without the Premier League title for the first time in several years, with the Italian inheriting a group of players already undergoing significant change following the departures of Bernardo Silva and others this summer.
The protracted nature of the negotiations has delayed City's ability to formally confirm their new head coach, though sources close to the talks suggest both clubs are keen to reach an agreement swiftly given the approaching start of pre-season preparations.