The former Barca midfielder, who played for the Catalan giants for eight years between 1996 and 2004, was reportedly spotted arriving at Camp Nou for a meeting this week.
Reports have suggested Gerardo Martino is unlikely to remain at the club after a season that looks set to end without silverware, with sections of the Spanish press suggesting Enrique could be the man to take over.
However, Celta chief Ricardo Barrios has played down speculation over Enrique's future.
"There is no unease here. Luis Enrique is the Celta manager," Marca quote Barrios as saying.
"I can't make any comment on that Barcelona meeting. As far as we are concerned, he is still the manager of the team and there is absolutely nothing else to say."
Enrique coached Barcelona B before arriving at Estadio de Balaidos via a spell at Roma.
Having taken over at Celta after their first season back in La Liga, the 43-year-old is on course to secure a top-half finish in his debut campaign.
