Monday's talks aimed at ending the players' strike which has disrupted the start of the Spanish league season have ended with no agreement reached.
Both sides will reconvene at the headquarters of the Association of Spanish Footballers (AFE) on Tuesday afternoon at 1600 local time (1500 BST) to discuss the proposals exchanged after Monday's meeting.
The AFE announced earlier this month that players from the top two divisions in Spain would go on strike for the first two rounds of the 2011-12 season unless an agreement with the Spanish League (LFP) was reached over the issue of unpaid wages.
The AFE want a guaranteed fund to protect players' wages in the event of their clubs being declared insolvent.
According to the AFE, clubs in Spain owe around €50 million in unpaid salaries to more than 200 players from the end of last season.
Talks between the two parties last week failed to find a resolution, leading to the scheduled opening round of Primera Division and Segunda Division fixtures being postponed at the weekend.
The AFE and LFP met again for more talks on Saturday and the third of three scheduled meetings took place at the LFP's headquarters in Madrid today.
AFE director Luis Gil sounded a pessimistic note after Monday's discussions, telling reporters in Spain: "The problem is not solved. I understand that people want to watch football, but we must think about the players who are suffering. I would be more optimistic, but I cannot.
"Presently, I can only speak of a strike for the second round of matches. And it will remain in place if we cannot find agreement on all points. We made another proposal and now must see if an agreement can be reached.''
The second round of Primera Division matches includes reigning champions Barcelona hosting Villarreal next Monday and Real Madrid travelling away to Real Zaragoza on Sunday.