Welsh rivals Cardiff and Swansea have never managed home and away wins since their bitter rivalry began in 1929.
Steven Caulker's winner for Cardiff settled last November's first ever meeting in the Premier League, under old boss Malky Mackay.
Solskjaer said: "The chance is there for us to make history and we are capable of doing it.
"I watched the first game on TV in Norway. I've watched the Premier and English League since I was 10, so I know all about the rivalry.
"We have all followed Swansea's adaptation through Roberto Martinez, Brendan Rogers and Michael Laudrup, so our local aim is to finish above them. That's what the rivalry is all about - it's a big one for us next weekend."
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