The Imps will travel to the Emirates Stadium looking to continue their incredible run in this season's tournament having become the first non-league team to reach the quarter-finals for 103 years.
Twelve-time winners Arsenal stand between them and a place in a Wembley semi-final, but Cowley insists that his side will attempt to play their usual game instead of parking the bus.
"If we get on the right side of the result, it would be the biggest upset in the history of the greatest cup competition in the world. [Arsene Wenger] has forgotten more than I know. He's a pioneer. We've got huge respect for him as a man and as a manager," he told reporters.
"I think all the pressure is on Arsenal, but we try to put energy and focus into our own team. We're not going to fear it. We're going to embrace it and enjoy it, but we'll go there with a game plan.
"We want to be us. We've got here because of our method and the way we play. It would be easy to park the bus, but that's not us."
Lincoln have already eliminated Premier League opposition in this season's competition, beating Burnley in the fifth round.