Sweden have never been beaten by England in a competitive fixture - a sequence of seven World Cup and European Championship encounters.
Olsson knows they must add to that sequence after losing 2-1 to the Ukraine in their opening group match on Monday.
The West Brom player said: "Our good record against England is something that is nice to have in the back of your head.
"We've done well against them and hopefully we can keep that streak going for a few more years.
"It is quite a lot of matches and you never want to be in the team that sees such a streak end.
"We also know that we need a positive result on Friday if we want to stay in contention in the group and that drives you on."
Olsson was quick to play down reports of disharmony in the Swedish camp.
He said: "I don't know where that has come from. One of our biggest qualities is that we are a very nice group and very happy together.
"We showed that during qualification when we were down after losing against Hungary but we came back and managed to qualify.
"What helped was the great atmosphere in this group and I think that is very unique."
Olsson believes new England head coach Roy Hodgson will inspire and get the best out of the current squad during Euro 2012.
Olsson can already see the same style and system which proved successful for Hodgson when in charge at West Brom being integrated into the England set-up.
He said: "The way England played against France is very similar to the way Roy Hodgson set the team up at West Brom.
"It's an organised team, they defend well and are good on the counter-attack with the pace they have up front from Oxlade-Chamberlain, Welbeck and Walcott.
"Roy is a top, top coach. I really enjoyed the time under him at West Brom. He is experienced and is good at inspiring players and he is a very nice man as well.
"That is important as well, that you connect with someone you are working with on a personal level as well and have that respect for him.
"That respect will make you go those extra yards for him and I'm sure the England players will feel the same."