Paco Chaparro (pictured) at Real Betis looks to be most at risk after his side were knocked out of the King's Cup by fellow strugglers Real Mallorca on Wednesday and lie 16th in the league with only six wins all term.
Another failure at home to Getafe on Sunday could spell the end for the former reserve team coach, who replaced Hector Cuper in December 2007.
"It was a big blow for all of us," Chaparro said after the 0-0 Cup draw with Mallorca, which condemned Betis to a 1-0 aggregate defeat.
Atletico Madrid's Mexican coach Javier Aguirre has also been feeling the heat.
Atletico have not won since Deember 20 and are languishing in sixth, nine points behind second-placed Real Madrid even though they have scored more goals than their city rivals.
Midfielder Paolo Assuncao said he understood the fans' unhappiness but said Sunday's match at home to Real Valladolid was a chance to put their season back on track.
"The supporters pay their entrance fee so they have every right to complain," the Brazilian said in an interview with Thursday's AS newspaper.
"We just have to get the win, whether we're playing badly or playing well. The team is in good shape now and we'll get back to winning ways."
Sevilla coach Manolo Jimenez needs a comeback win in Thursday's King's Cup quarter-final, second leg against Valencia to help dispel any doubts over his future before his side travel to Sporting Gijon for Sunday's league clash.
If they fail to overturn a 3-2 deficit from the first leg in Valencia, their chances of winning a trophy this season will be effectively gone following their exit from the UEFA Cup.
Real Madrid are looking for a sixth straight league win at Numancia on Saturday to keep alive their slim hopes of catching Barcelona, who play at Racing Santander on Sunday.
Real's Portuguese central defender Pepe said the champions would fight all the way to hold on to their title.
"Barcelona is strong and playing some great football but they will have their moment of crisis," he said in an interview with Marca newspaper. "We have to be ready to cut the gap in points when they slip up."
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