The Gunners asked about Sterling in a potential swap deal for Alexis Sanchez, but Guardiola shut down the move.
"Raz [Raheem] is staying here," Guardiola told a news conference.
"The club trust him, that is why we have invested a lot of money in him, so the players we have are going to stay.
"If they want to leave they are going to leave, but he wants to stay. If players want to leave they have to ask the chairman, but there is no chance of that. He is going nowhere."
The 22-year-old has started the season in scintillating fashion for the Sky Blues, having scored five goals in five Premier League appearances.