The 35-year-old’s contract with the French champions expires this summer and he could become a free agent.
“At the moment we are negotiating with Messi his renewal,” Campos told Telefoot on Sunday.
However, since winning the 2022 World Cup in Qatar with Argentina, reports claim that contract talks have been more complex.
“I’d love to keep him in the project, I can’t hide it,” Campos said. “We are negotiating to achieve that goal and for him to continue with us.”
Messi joined PSG in the summer of 2021 after Barcelona did not renew his contract due to financial problems.
The Argentina captain struggled in his first year at PSG but has been impressive this season, scoring 15 goals and setting up 14 more in 24 appearances across all competitions.
He scored the winner in Saturday’s 2-1 league triumph over Toulouse.
Campos said: “I remember that I told Messi during half-time of the game against Montpellier: ‘You have to drag everyone with you’ and he [Messi] responded: ‘no worries’ and he had an exceptional second half.”
There has been speculation that Messi would return to former club Barcelona or consider a move to North America to play in Major League Soccer.
A seven-time Ballon d’Or winner, Messi won his first World Cup after helping Argentina beat France on penalties in the final in Qatar.
He was awarded the Golden Ball award as the best player of the tournament.