LFP president Jose Luis Astiazaran said on Thursday there had been "no major progress" in finding a solution to the spat which blew up last month after the league urged Spain's Socialist administration to scrap a rule that one La Liga game per matchday should be shown on free television.
The LFP argues that the move would strengthen clubs' bargaining power in negotiations on audiovisual rights with media firms. It also wants guarantees about how much cash it is entitled to receive from betting and lottery revenue.
Astiazaran said on Thursday he saw "very little chance" of finding a resolution that would prevent the suspension of matchday 30 on the weekend of April 2-3, when La Liga leaders Barcelona are due to play at Villarreal and second-placed Real Madrid host Sporting Gijon.
However, he said the LFP was still open to dialogue.
"The national team is playing on Friday in Granada and we will more or less all be there," he told reporters. "Let's see if we can find some common ground."
The league, which represents first and second division clubs, says the free game will not necessarily be scrapped but it wants the obligation to show it to be dropped.
It has the backing of the Spanish football federation (RFEF) but six of the 20 clubs in the first division - Sevilla, Villarreal, Athletic Bilbao, Espanyol, Real Zaragoza and Real Sociedad - filed a legal challenge in a Madrid court on Wednesday in an attempt to block any postponement.
The six clubs believe a strike would be "disproportionate, inopportune, against the interest of clubs, the competition and supporters and, what's more, against the law," Sevilla said on their website.
Astiazaran said it was not good to have division among the LFP members, noting the decision to threaten a postponement of matches had been taken democratically at a meeting last month.
If the games are postponed, the earliest they can be played would be June 11-12, three weeks after the scheduled end of the season.
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