Vieira rejects Real move
The French midfielder has been a long-term transfer target for Real and his future has been the subject of constant speculation.
The 25-year-old has been linked with a big-money summer move to El Santiago Bernabeu, but Vieira insists he is happy to stay at Arsenal.
Vieira played an instrumental role in helping Arsenal to a domestic Double this season and he is planning for future success with the North London outfit.
"My contract with Arsenal is running for the next two years and everything is perfectly clear in my head," he said in a press conference at the France training camp at Clairefontaine.
"I don't intend to leave.
"We have had a fantastic season, particularly in the Premier League. We have achieved two of the three goals we have set ourselves.
"We could have done a little better in the Champions League and it leaves some regrets as we had a great team."
Asked if he had considered a move to Real Madrid to join up with French compatriot Zinedine Zidane, Vieira admitted he had thought about it.
"When a club like the Real Madrid want you, obviously you have to think about it and it's what I did," he added.
"But, after a while, I made up my mind and I have realised it was best for me to stay with Arsenal."
The midfield powerhouse, who is now concentrating on helping France retain their World Cup trophy, admitted that he was tired after a hectic season and he is set to be left out of Saturday's friendly with Belgium.
"I need a few days to rest and I'll train on my own for the next two or three days. But I'm certain I'll be fit again very soon," he concluded.