The Magpies suffered a demoralising defeat to newly promoted West Ham last weekend but the former Manchester United defender is hoping to quickly get back on track
The Magpies slipped to tenth in the Premier League as they suffered a 1-0 loss at the hands of the Hammers at St James' Park last Sunday.
But Simpson believes the upcoming clash with the Swans represents a chance to immediately get back to winning ways.
"We need to bounce back and Swansea is a good opportunity," Simpson told Sky Sports. "With it being a home game, it'd be good to put some points on the board.
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"They've got different threats to West Ham. They are more technical and want to play quicker football, but that will suit us, I think.
"They will come and have a go at us, and when teams do that we have got the players up front and on the break to create problems for them."
The visit of Swansea sees the return of Newcastle old boy Wayne Routledge, a man Simpson still counts as a close friend.
"I chat to Wayne on a weekly basis and he is very happy at Swansea," Simpson added.
"I'm sure he is looking forward to coming back up here and playing against the lads, but if I play against him I will have to kick him as usual!"