The future of the Argentina forward has been the subject of much speculation recently, following reports that he had fallen out with Enrique.
Messi has been linked with a move to Barclays Premier League champions Manchester City and leaders Chelsea, but Enrique does not want to see the four-time former world player of the year leave the Nou Camp.
“I don’t know what the future holds for us,” the 44-year-old told the Spanish media on Wednesday. “We all think that Messi will be at Barca in the next few years and that is what all the cules (Barca fans) want.
“The thought of having a team without Messi is not even something we contemplate.”
Messi, who is Barca’s all-time top scorer in all official club competitions, is under contract with the Catalan giants until June 2018.
He has been instrumental in helping Barca win 21 trophies, including six Primera Division titles and three Champions League crowns.
Barca overcame champions Atletico Madrid 3-1 on Sunday night to provide some much-needed cheer after an unsettled start to 2015.
A number of players are said to be unhappy with Enrique’s tactical and coaching methods since he replaced Gerardo Martino in the summer.
But Enrique, whose side take on Elche in the second leg of their Copa del Rey last-16 tie on Thursday holding a 4-0 advantage from the first leg, insists his squad is united.
“We are running away from controversies and we are looking to find the best atmosphere possible,” he said. “The changing room is united.
“This is what we are looking for, even though we know that things on the outside can change within five seconds.”
The Catalan club began 2015 with a 1-0 defeat to Real Sociedad and the following day sacked sporting director Andoni Zubizarreta, with former captain Carles Puyol leaving his role as Zubizarreta’s assistant hours later.
When asked about reports in the local media that former player Jose Mari Bakero was the leading candidate to replace Zubizarreta, Enrique said: “This is a question for our president (Josep Maria Bartomeu).
“All I can say is that I have a good opinion of him.”