Talks continue over Spanish player strike
"The problem isn't resolved," AFE spokesman Luis Gil told reporters after the fourth meeting between the sides over the last week.
"I understand people want to see football but you have to think about the players who are having a bad time. I would like to be more optimistic, but I can't."
Last weekend's first round of fixtures for the new season were postponed because of the strike, which has also been called for the second round of games in the top two divisions.
The union is demanding greater protection for players' wages that have not been paid at clubs that have gone into financial administration.
The AFE say around 50 million euros is owed to 200 footballers from the end of last season.
The president of the LFP, Jose Luis Astiazaran, said: "We have detailed some proposals and the negotiating teams will continue working."
The union and the league, who represent the 42 professional clubs in the top two divisions, will meet again on Tuesday.