The Chile international has long been rumoured to be seeking a way out of the Emirates Stadium, and on deadline day, it appeared that he was on the verge of becoming a Citizen.
However, the deal ultimately did not go through, leaving Sanchez still on the books of Arsenal and Sterling still at City until January at least.
Guardiola told reporters on Friday: "When we started to speak with Arsenal in the last days, they wanted to make a swap with Raz.
"They talked to me and I said 'no chance. zero chance. Not one per cent chance we will swap Raz because I trust a lot in him'. Twenty-two years old, English player, there is a lot of room to improve.
"The only deal we would do was cash. In the end Alexis stayed in Arsenal. I don't know what will happen in the winter. Sometimes deals work, sometimes not."
Man City host Sterling's former side Liverpool in the Premier League this Saturday.