The Gunners head into the international break on the back of a 6-2 thrashing of Blackburn which saw them become the highest scorers in the Premier League.
With matches in hand on the top three, Arsene Wenger believes his team are now well placed after recording six straight wins in all competitions since losing away to both Manchester clubs.
Former United defender Silvestre, who made the switch from Old Trafford last summer, has watched from the bench most of this season, his only appearance so far coming as an experienced member of a youthful Carling Cup side.
However, the 32-year-old Frenchman - who won the 2008 Champions League as well as four domestic titles while with United - has seen enough to convince him Wenger's youngsters have what it takes to make a sustained challenge.
"In those two defeats, we learned that we are not far from being a winner," Silvestre told Arsenal TV Online.
"We scored goals away from home which is good and I am looking forwards to the big games again this season to test ourselves.
"We play very good football and I hope it will pay [off]."
Silvestre added: "It is about being mature and the details.
"If you look at the way we conceded two goals at the weekend, if we can get rid of those moments, then we will have a real chance.
"We are not far from it."
Silvestre's impact last season was hampered by a tendon problem, although he did recover in time to feature in the Champions League semi-final defeat to his former club.
The defender, who can play both in the centre or at full-back, opted to top up his sharpness for the reserves in a 2-0 win over Chelsea on Monday night.
Silvestre hopes he will soon be challenging for more first-team action.
"After the Blackburn match, I wanted to play, and play 90 minutes, which is good to keep the fitness up," he said.
"You cannot match a game with training, so I am pleased.
"I had two big injuries last season, now I look better and hopefully I can play my part to help the team to be successful.
"You need consistency, to play more games to be at your best.
"Any chance I get, I will give 100%."
Arsenal will have some 20 of their first-team squad away on international duty - including Theo Walcott, Kieran Gibbs and Jack Wilshere all for England Under-21s against Macedonia at Coventry's Ricoh Arena on Friday night.
However, Robin van Persie, 26, will not be travelling to Australia with Holland, who like England have already qualified for the World Cup, as his wife is expecting their second child.