Swansea have won their last two meetings with the Gunners, including their 2-0 win at the Emirates Stadium last month thanks to a Michu brace.
And Laudrup expects Arsenal to be thirsting for revenge after they were booed off following that defeat.
"It's never nice to have lost at home and they will remember our game - they will want revenge," he said. "It looked bad after they played us - they were 10th. For a club like Arsenal, that's a disaster.
"But they won three games consecutively and they are back again.
"They are many years without a trophy and they know the league is not a trophy for them. They have two left so they will come with their best possible line-up and do everything to beat us."