The 35-year-old, who spent 11 years in England with Manchester United and Arsenal, is a free agent after leaving Werder Bremen in the summer.
The Frenchman is currently training with United in an attempt to build up his fitness and he believes that he still has the quality to play at the highest level.
Silvestre told MUTV: "I came a few weeks ago and had a chat with the gaffer just before the League Cup game. I said I was coming back to Manchester until Christmas and he said, 'Come and train and stay fit until you move to somewhere else'.
"When you are training with the lads you feel like you are still capable of playing in the Premier League. I am fit, that is the main point, and I still have the hunger for the game. So this level is still the level that I am targeting."
It has been suggested that Silvestre could join United on a short-term deal.