Reports in Spain on Friday have said that initial talks have opened between the club and the five-time Ballon d'Or winner over the prospect of extending his deal at Camp Nou.
Messi's father, Jorge, is believed to have flown to Barcelona to take part in discussions as he looks to broker a deal that will keep the 29-year-old at the club until 2022 on a wage that will make him the world's best-paid player.
Luis Enrique says any confirmation of an agreement would be a cause for celebration but was reluctant to speculate on whether the talks will be successful.
"It's good news, of course," he told a media conference ahead of Barca's LaLiga game with Osasuna on Saturday.
"I'm quite relaxed about his dad being here. The day that Messi's renewal is announced will be a day to celebrate. At the moment, I don't dare predict if he will renew or not."
Messi's contract is due to expire in 2018 and rumours of a potential transfer elsewhere in Europe have refused to die down in recent months, with Manchester United and Manchester City among the clubs tentatively linked with a bid.