“We’re talking fantasy football, a situation that cannot be approached at Inter for many reasons,” Conte said after Inter beat Genoa 3-0 to move second in Serie A.
Six-time Ballon d’Or winner Messi, 33, has spent his entire professional career at Barcelona with his contract due to expire in 2021.
“I don’t think there is a madman in the world who does not want Messi, but he is really far from us and what we want to build,” added the former Juventus and Chelsea coach.
Inter CEO Giuseppe Marotta also brushed aside talk that the northern side wanted Messi to rival Juventus star Cristiano Ronaldo.
“Leo is not our goal and I don’t think he wants to leave Barcelona,” said Marotta.
Conte, meanwhile, said he hoped that the club could reach agreement with Manchester United concerning on-loan forward Alexis Sanchez, so that he could play the Europa League with Inter.
Sanchez, sidelined for months with a knee injury, scored on Saturday with his former United teammate Romelu Lukaku getting a brace.
“I hope that the club can resolve the situation because so far, Alexis hasn’t been available much,” said Conte.
“To have a quality alternative in attack would be vital for us.”