The Brazil forward has been suffering from mumps, depriving Barca of one-third of their lethal attack that includes fellow South Americans Luis Suarez and Lionel Messi.
The trio scored a Spanish record 122 goals in all competitions last term as Barca swept to a treble of Champions League, La Liga and King's Cup titles.
Neymar missed this month's European and Spanish Super Cups, as well as last weekend's 1-0 win at Athletic Bilbao in their opening match of the campaign but could return to face Malaga at the Nou Camp, Luis Enrique told a news conference.
"He seems in very good shape, practically recovered or recovered and in normal condition for a player who was unable to train for almost two weeks," Luis Enrique said.
"He is a player who weighs very little, very thin, and he can get back to full fitness very quickly," added the former Barca and Spain midfielder.
"His GPS data in training are among the best in the team and that means he has a chance of participating tomorrow.
"A player with a different physical makeup would practically be ruled out.
"He has been training very well and tomorrow we'll see what decision we'll take."
Midfielder Sergio Busquets, who took a knock to the ankle in the Bilbao game, also looks likely to be available for Saturday's match, Luis Enrique said.
"He has been able to train with us since yesterday and he is in very good shape.
"We'll see tomorrow exactly how he is feeling and if he can be included in the team."
Qatar-owned Malaga managed to hold Barca to a 0-0 draw at the Rosaleda last term and surprised the Spanish and European champions by beating them 1-0 at the Nou Camp, one of only two La Liga defeats there all season.
However, they have sold some of their best performers during the close season and are not expected to mount the same kind of challenge this time around.
(Writing by Iain Rogers, editing by Sudipto Ganguly)
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