The six-time Ballon d'Or winner has been a free agent since running his Blaugrana contract down at the end of last season, with negotiations ongoing to come to an agreement over an extension.
Barca are still said to be confident of getting Messi to commit his future to the club, but they have navigated their pre-season preparations without the Argentine while he is not under contract at Camp Nou.
Messi was recently pictured on holiday in Ibiza with former Barcelona teammate Luis Suarez, meaning that Ronald Koeman's side reported for training on Monday morning without the attacker present.
Barcelona are under pressure to offload several big earners before being able to tie Messi down to a new deal, but AS reports that the Catalan giants are determined to have the 34-year-old on the books in time for their La Liga opener with Real Sociedad on August 15.
Messi struck four goals and set up five more in seven Copa America matches for Argentina en route to the trophy, and he boasts 672 strikes from 778 games for Barcelona.