Mediaset says Laporta met with Koeman at a restaurant in Barcelona on Thursday to analyse the team's situation after Tuesday's 3-3 draw at Levante.
Club sources downplayed the importance of this meeting and stressed that the two men often get together to discuss the team, but on this occasion the gathering may have a special significance as Koeman's future is up in the air.
The two men were joined at the restaurant by the club's sporting vice president, Rafa Yuste.
Laporta wanted to hear Koeman's opinion first-hand about Barcelona's recent results and ask for an explanation as to why the team dropped points against Granada and Levante, despite taking the lead in both games.
The Barcelona president is not expected to make a decision on Koeman's future until the end of the season, but in Thursday's meeting he wanted to boost his coach's morale and find out whether he is willing to continue planning the team's future along with Mateu Alemany and Ramon Planes.