On Tuesday, the six-time Ballon d'Or winner sent Barcelona a fax requesting that he be released from his contract in order to talk to other clubs and end his 20-year association with the Blaugrana.
Messi has been unhappy with how the club has declined this season, losing the league to Real Madrid and then being dumped out of the Champions League after an 8-2 defeat against eventual winners Bayern.
He has reacted negatively to how the team is performing on the pitch and how the club is being run off it, and previously clashed with former director of football Eric Abidal earlier in the season.
But facing the media on Wednesday, Planes sought to play down the situation, saying: "The truth is that it was important news, but we thought and have always said it, the president and I think of Leo Messi as the future of Barcelona under construction.
"We all have to draw conclusions from what happened and the idea is to build a team around the best player in the world."
The 33-year-old currently has a release clause of €700m, but previously had a stipulation in his contract allowing him to leave for free this summer, which expired at the end of May.
But Planes says there is no dispute between the player and club with regards to any clauses.
He added: "We do not contemplate any exit from Leo at the contractual level.
"We want him to stay. We have to have great respect for him. He is the best in the world, in history. The future is positive, we must speak optimistically. We must build everything. The Barcelona we want. It's our idea.
"It is a marriage and they have given a lot. People see the marriage of great players with Barcelona and this has given many joys. We have to fight to keep it going.
"We are working on building a new Barcelona. All the plans are to make a winning team, with youth, we are regenerating it, accompanied by great players and with respect for those who have given so much.
Ronald Koeman is the new head coach of Barcelona, having taken over from Quique Setien following the devastating loss against Bayern.