The move comes only a day after the Spanish High Court agreed to open proceedings against Rosell over an alleged misappropriation of funds from the Neymar transfer from Santos in the summer.
Rosell, who took over from old foe Joan Laporta in 2010 after winning a landslide vote, has denied any wrongdoing in the Neymar case, but could face imprisonment for anywhere between one and eight years if found guilty.
Barca vice-presidents Josep Maria Bartomeu and Javier Faus met with Rosell at his home this morning and will join the Barca president at the extraordinary meeting later on Thursday, along with deputy president Joanjo Castillo, general director Antoni Rossich and communications director Albert Montagut.
Rosell's current mandate runs until 2016 and if he does step down on Thursday, Bartomeu will take over until the next elections.
Meanwhile, Laporta has hinted on several occasions that he would be interested in running for a second spell in charge of the Catalan club.