Enrique has won eight trophies in two and a half years in charge but is out of contract at the end of the season and is in no rush to renew, with the club's focus on securing new deals for Lionel Messi and captain Andres Iniesta.
Barcelona daily Sport reported on Wednesday that Enrique's assistant Juan Carlos Unzue is his preferred choice to take over should he leave, whilst Sevilla boss Jorge Sampaoli has also been heavily linked with a move to the Camp Nou given his fine first season in Spanish football.
"I don't have anything to say," Enrique replied when pressed on his future and whether Unzue, who has barely any senior managerial experience, could handle the role.
However, Enrique insisted his relationship with the squad is as good as ever in his third season in charge.
"This is my third year here and I see the same desire, same eagerness and will to want to keep making history and winning titles. I see the same hunger and I would even say it is greater with every passing season."
Barca remain well-placed to land more trophies under Enrique's watch as they welcome Real Sociedad to the Camp Nou on Thursday for the second leg of their Copa del Rey quarter-final holding a 1-0 first-leg lead.
The Spanish champions are also only two points adrift of La Liga leaders Real Madrid, although Madrid also have a game in hand, and face Paris Saint-Germain in the last 16 of the Champions League.