Messi became the all-time leading La Liga goalscorer by scoring a hat-trick in Barca's 5-1 thrashing of Sevilla on Saturday.
Argentina captain Messi was coy over his future during an interview with newspaper Ole in his homeland this week, stating his desire to remain at Barca before adding that "things don't always work out as you want them to".
But Luis Enrique preferred to avoid the speculation, saying his focus was on the 27-year-old superstar's ability.
"I like living the present and this is marvellous with the best player of the history, to me, in our team," he said.
"We are not going to feed the talking. I trust his quotes I have heard from him and we have to keep on working for improving and trying to raise our level for reaching titles, which is the target we work on."
Messi opened the scoring in Barca's rout of Sevilla before adding two late goals to break Telmo Zarra's record of 251 goals.
Luis Enrique said the attacker was a unique talent.
"Everybody has the clarity of telling I haven't seen a player like Lionel Messi and I am fortunate for training and seeing him every day at the training field," he said.
"And even sometimes he surprises you with some good performances. There is not comparison with other players I have seen along my life. He is unique."
