Patrice Evra said the nature of the threats meant he had to be protected by bodyguards.
Luis Suarez, recovering from right knee surgery, said it was "complicated" to talk about players joining Barcelona at this time of crisis with the coronavirus pandemic.
Barcelona's defeat to Valencia raised early doubts about Quique Setien's appointment and gave Real Madrid the chance to move three points clear at the top.
Valencia will provide Barcelona's new manager Quique Setien with his first true test and an opportunity to make his mark.
Barcelona issued a press release saying the surgery on Luis Suarez was for an "injury to the external meniscus of the right knee".
Luis Suarez and Lionel Messi are part of the potent Barcelona strike force that keeps them in the top slots of Spanish and European football.
A mistake by Barcelona's usually excellent goalkeeper Marc-Andre ter Stegen gifted Real Sociedad an equaliser in a thrilling La Liga contest.
Luis Suarez scored a goal with his backheel in a La Liga match against Mallorca and called it the "best goal of my career".
Argentina and Uruguay will face off on Monday evening in a match expected to pit Lionel Messi against his Barcelona strike partner Luis Suarez.
Trouble returned to Real Madrid after they endured their first La Liga defeat of the season at newly-promoted Real Mallorca.
Barcelona are second in the La Liga table, two points behind Real Madrid, following their 4-0 win over Sevilla at Camp Nou.
Barcelona came from behind to beat Inter Milan in a thrilling Champions League contest at Camp Nou on Wednesday.
Granada vs Barcelona: With seven points on the board, this is Barcelona's worst start to a season since 1994.
Lionel Messi and Luis Suarez were in the stands as Barcelona beat Real Betis 5-2 at Camp Nou on Sunday.
Substitute Aritz Aduriz scored a sensational late volley as Athletic Bilbao beat Barcelona 1-0 in La Liga's first match of the new season.
Luis Suarez scored the winner in the 89th minute in front of nearly 99,000 people, who packed the stands to see new signings Antoine Griezmann and Frenkie De Jong.
Lionel Messi, who turns 32 in June, Sergio Busquets, who will be 31 in July, and Gerard Pique, already 32, have hung on, driving the club through fresh cycles of success.
Luis Suarez had bit Italian centre-back Giorgio Chiellini on his shoulder in World Cup 2014.