The 48-year-old is believed to be on a five-man managerial shortlist drawn up by the Catalan club, along with Xavi, Jordi Cruijff, Antonio Conte and Andrea Pirlo.
According to Goal, Barca have spoken directly with Martinez about the managerial position at Camp Nou after deciding they will relieve Koeman of his duties imminently.
The report also states that the Spaniard had been identified as a managerial candidate by club president Joan Laporta before he was appointed to his role in March.
Martinez will now consider his position as Belgium boss as he had intended to lead the Red Devils at the 2022 World Cup in Qatar.
It is understood that Martinez could terminate his contract with Belgium, which would cost around £1.5m, though this is a figure Barcelona would be prepared to pay should they make a formal approach for his services.
The former Swansea City and Wigan Athletic manager has been out of club management since he was dismissed by Premier League outfit Everton in May 2016.
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