Vieira has been linked with Arsenal, Tottenham and Notts County in recent months.
He told L’Equipe: “You never know what can happen, but I have made my decision. I will stay at Inter. I am fine, I have no reason for leaving.
“The end of last season was difficult for me as the coach didn’t trust me anymore. But his words have changed. I have resumed training sessions without any physical problems.
“I have played a lot during friendlies, much more than I expected. However, I have received no guaranties. Physically I am perfectly fine. Now I just need to play.
“Indeed, Tottenham showed interest in me joining them. Harry Redknapp, who I respect a lot, proposed me a challenge that could have been exciting on a sporting level.
“But it would have been very difficult on a human level. For one or two seasons with Spurs I could not see me wasting nine years spent at Arsenal.
“Frankly, there has been nothing concrete with Arsenal. With Arsene sometimes we have phone calls, but that’s all.”