Manchester City, Manchester United and Juventus are hoping to sign last season's top scorer in the Premier League, whose contract expires next summer.
But Wenger has remained defiant by declaring van Persie, who is valued around £20 million, is staying in north London.
"There is nothing to elaborate. The options are clear - we want to keep our players," he said.
"I would be happy for him to stay in the English Premier League - at
Wenger has promised more new recruits at Emirates Stadium after adding Lukas Podolski and Olivier Giroud to his squad this summer.
Spain winger Santi Cazorla and France midfielder Yann M'Vila have been linked with moves to Arsenal.
"I won't talk a lot about transfers because it is a very fragile and secret subject," Wenger added.
"We bought Giroud and Podolski but we are not at the end of it - we will still bring players in."
Van Persie's name has been included alongside his team-mates' in Arsenal's official squad numbers list for the 2012/13 season.
The 28 year-old has been allocated his usual No 10 shirt - although his expected departure could free up the shirt for Podolski, who has yet to be assigned a number. Giroud will wear No 12.