The coach is not concerned about speculation linking the Brazil star with a move away from Camp Nou and says he will be available to return to the team against Athletic Bilbao
The Brazil forward's existing deal is due to expire in June 2018 and Manchester United, Real Madrid and Paris Saint-Germain are believed to be keeping a close eye on his situation at Camp Nou.
But Luis Enrique expects the 23-year-old to renew his contract with the Spanish and European champions.
"I believe Neymar will end up signing a new contract here," the Barcelona boss said at a press conference on Tuesday.
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Neymar missed Saturday's 2-1 win over Malaga due to a minor hamstring problem, but Luis Enrique expects him to be fit for Wednesday's Copa del Rey quarter-final second leg against Athletic Bilbao.
"Neymar is fine," he added. "There is no risk with him. He has trained and is in perfect condition."
However, Barca may have to do without captain Andres Iniesta, Sergio Busquets and Arda Turan due to illness.
"Sergio, Arda and Andres have the flu," Luis Enrique added. "We will make a decision about them on the day of the game."
Copa holders Barca lead the quarter-final tie after goals from Neymar and Munir El Haddadi gave them a 2-1 first-leg win at San Mames.