The England international is reportedly a target for new Gunners manager Mikel Arteta, who worked with him for three and a half years at the Etihad.
Stones has struggled for consistency since his £47.5m move from Everton in 2016 – and Guardiola recently challenged the 25-year-old to prove he can help fill the void left by Vincent Kompany.
Facing questions for the first time since links with Arsenal emerged, the City manager said: “I’m not going to talk about the rumours, the players linked with us or the other clubs.
“We’ve been linked with a lot of clubs. I’m not going to answer.”
Stones has struggled for fitness and form during Guardiola’s time at the club – and would have found his position under threat had City secured the signing of Harry Maguire in the summer.
Guardiola is expected to try to strengthen in central defence at the end of the season after failing to replace Kompany, who walked away last May.
Earlier this month Guardiola challenged Stones to realise his potential.
“We tried to help him,” he said. “We tried to do the best to help him since the first day of the three and a half years we are here. We do everything for him.
“He has the conditions to do it, but to be the best central defender you have to play one entire season, every three days being there.
“It’s difficult to reach the potential that he has, he has to be at the level to play regularly. The last three seasons and a half he could not do it.
“I don’t know why he is not able, we are not able, to be a regular for a long, long period because he’s a young player.
“He’s still young. As a player he has his future in front of him, it depends on him. It’s in his hands and in his head to become one of the best.”