Alastair Cook and Jonathan Trott will resume at the crease on Saturday, and Swann does not see any reason why England's batters cannot match Australia's performance on a pitch offering little to the seam bowlers.
"It's a tough flat pitch and come the morning the ball will be softer," he told reporters.
"It should be a great pitch to bat on tomorrow - I don't see it breaking up. The main part of pitch will stay true.
"We will bat all day tomorrow into day four, get a lead then bowl them out. I don't see why we shouldn't approach this with any fear. We've got some of the best batsmen in the world."
Swann picked up his 17th Test five-wicket haul during Australia's innings, recording figures of 5-159.