Talks progress in bid to avoid players strike
The AFE have officially called for industrial action over unpaid wages, particularly in the third and fourth tiers of the game, that would affect matches between April 16-19.
"There isn't an agreement but a part of the problem has been been resolved," AFE president Luis Rubiales told reporters.
"Things have moved forward but not far enough. We hope to reach a solution quickly."
Spain's Sports Minister Jaime Lissavetzky said the talks between the AFE, the league, the federation and the government had been constructive.
He spoke of plans to use pools' revenue to help resolve the situation, and was positive an agreement would be reached on Tuesday.
"It's a problem that extends to the whole of European football," he said. "The system isn't adequate for the future and for this reason I am pushing for a new law for professional sports people.
"One of the key elements is to create an independent regulator which will attempt to achieve a balance between income and expenditure."
If the strike went ahead it would affect the matches between La Liga leaders Barcelona and city rivals Espanyol, and second-placed Real Madrid's game against third-placed Valencia, among others.
As well as damaging the credibility of Spanish soccer it would place additional strain on a calendar that is already tight because of this year's World Cup.
Spain still has not fixed a date for the King's Cup final between Atletico Madrid and Sevilla.