The Greeks may have won all of their domestic matches this season but are yet to record a victory on 12 visits to England, which have included heavy losses at the likes of Manchester United, Chelsea, Newcastle and Liverpool.
Arsenal beat Olympiacos 3-1 in London three years ago, maintaining their 100% home record against them in recent Champions League meetings.
Silva, though, believes his current squad have what it takes to recover from their opening Group F defeat against Bayern Munich.
"We are prepared to get the best result we can
We know it will be a difficult game, how big a team Arsenal are and respect them, but we believe in our own strengths and are ready for a strong game," said the former Sporting Lisbon coach, who took charge in Athens over the summer.
"We are going to come here and show our best self, to show what we can do."
Silva continued: "We have analysed the jobs which Arsenal do well and will try not to make mistakes and match what we have done in training."
Arsenal lost their opening European fixture away to Dinamo Zagreb, who were expected to be scrapping it out with Olympiacos for the Europa League place.
Victory over the Gunners, however, would blow the race for qualification wide open.
"If you asked people who would be the first two in the group, people would say it is Bayern and Arsenal, but football is not like this - there are no rules to say the favourites must win all of the games," said Silva.
"We did not manage to win against Bayern, and yes the Dinamo win over Arsenal has made it more difficult for us, but we have our own ambitions and there are no limits to them.
"You have to go for it and we hope that we can change the situation in the group."
Midfielder Alejandro Dominguez feels there is plenty of confidence in the squad
"W e believe that we can do it as a team
Everyone has prepared well for the game and we hope to be able to prove it regardless of the stats that Olympiacos has here," he said
"We hope Tuesday will be a big day for us and we can get a positive result."
Source : PA