Robert Lewandowski started pre-season training at Bayern Munich on Wednesday amid a report that Barcelona believe they can sign the World Footballer of the Year before the end of the week, reported dpa.
Lewandowski, 33, had his first training unit the day after undergoing fitness tests in Munich.
However, Lewandowski has made it clear in the off-season that he wants to leave Munich after eight years in summer despite a contract until 2023.
Bayern bosses have so far said they won't let him go. But they are reportedly ready to listen to offers of €50 million ($50 million) or more, and according to reports Barca are planning a final €50 million offer plus add-ons.
Spanish paper Mundo Deportivo said Barca believe they could finalise a deal this week.
Bayern are du to present their squad to fans at the Allianz Arena on Saturday before going to the United States for a week from Monday onwards.
The season opens for the Bundesliga champions with the Super Cup against Cup winners RB Leipzig on July 30.