The result has left Barca's title pursuit hanging by a thread and afterwards Koeman conceded his job future could now be in doubt.
Mundo Deportivo says Laporta wants to meet with Koeman face-to-face to consider the team's situation.
Much of the growing doubts around Koeman involve not only their sudden form slide, but also the Catalans' failure to take points off their direct rivals in the LaLiga title battle.
There is no set date for the meeting because the team and the technical staff have two days off - Wednesday and Thursday - and then it is time to prepare for the Celta Vigo match, while the president is working on various fronts and has on the horizon the trip to Göteborg for the final of the Champions League for the womens team next Sunday.
Laporta wants Koeman to tell him personally where the progress of the team stands and about some of the coach's tactics.
- updated May 13