The 23-year-old has only started seven games this season, with the former Udinese star’s only goal coming in the Champions League.
The Reds were reported to be leading the race to sign Sánchez, but his agent Fernando Felicevich insisted the forward would not be leaving Camp Nou.
“Alexis will stay in Barcelona,” Felicevich told todomercadoweb.es.
“He has no reason to leave as he is in the best team in the world. Barcelona will not sell Alexis in any case. He has returned after injury and played well.”
Sánchez has scored 16 goals in 57 appearances for Barcelona after joining from Udinese in a €26m deal in July 2011.