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 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 50million euros 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 La Liga 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 will take place at the LFP's headquarters in Madrid on Monday, beginning at 1200 local time (11am BST).
The second round of La Liga matches includes reigning champions Barcelona hosting Villarreal next Monday and Real Madrid travelling away to Real Zaragoza on Sunday.