The coach would like to see the Ballon d'Or winner keep turning out for the Camp Nou side for at least another decade, but says it may not be possible
Reports in Spain suggest Barcelona are preparing to tie the five-time Ballon d'Or winner down to a new six-year contract, which would keep him at Camp Nou until the age of 35.
And, while Luis Enrique would love to see Messi remain at the club beyond that potential deal, he accepts that age eventually affects all players.
"I'm a coach and a good coach, I think, but not a magician," he told a news conference on Saturday.
"Lionel Messi is going to be the greatest player as long as he wants to, but there will be a time when age affects everybody.
"I'd like it to be until he's 40 years old, but I don't have a scientific basis to comment any further on that."
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Messi has netted 20 goals in all competitions since the turn of the year and is now six behind team-mate Luis Suarez in the Liga scoring charts.
Asked whether the 28-year-old is capable of topping that list come the end of the season, Luis Enrique added: "Of course, he is capable of doing anything.
"But he is totally focused on what he's doing, focused on achieving things more on a team level - not just him but the rest of the team. That's what makes me optimistic.
"I'm more concerned with collective targets, but if collective targets are met it's because individual targets are being met as well, and certain players will benefit from that.
"I think he's really focused on team objectives more than anything else."
Barca - eight points clear of Atletico Madrid at the summit - visit Eibar in La Liga on Sunday.