Silvestre, who once nodded in two goals for United against Liverpool, says the Gunners must use their heads in order to beat the Reds.
The French international defender said: “We are lucky we are still in the race because our eight-point difference could have been even bigger.
“But we see each week there are bad results among the top teams and none of them have pulled away.
“We are still in it. We have been behind when I was at United, and one season Arsenal won when they were 13 points behind, so you never know what can happen.
“United made a bad start last season and won the title.
“When we drew at Middlesbrough Saturday lunchtime we were the first team to drop two points and were very upset — but then the others did it, too.
“Chelsea drew at home to West Ham, United dropped points and Liverpool. The level of every team in the league is very high and every team can beat the Big Four. We can be closer to Liverpool by beating them on Sunday.”
Silvestre added: “When I was at United, there was a very big rivalry with Liverpool, but Arsenal v Liverpool is very strong as well.
“My first game for United nine years ago was against Liverpool. I arrived on Thursday at Manchester airport, trained with the team on Friday and on Saturday lunchtime we were playing at Anfield.
“I thought that if all the games were like this, it was going to be a tough season, even though we won 3-2. And four years ago, I scored two goals at Old Trafford to beat them, which is a special memory for me.”