Clarke, Australia's captain, has been in superb form over the past 12 months and Swann believes that England must execute their plans well to stop the batsman from having a big impact in the series.
"He was their form batsman in England in 2009, although he didn't have such a good series in Australia," Swann told ESPNcricinfo.
"The year he's had has been phenomenal, so we'll be hoping to cut the head off the serpent if you like, as a captain. The two Ashes series I've played, and one of the main reasons we've won, is because we've been able to make some of their best players have poor series.
"That's what you need to do to win big series, make sure the match-winners in their team don't have a chance to perform. We'll have two or three players on their team we'll definitely be looking at to keep especially quiet - although you hope everyone on the opposition has a poor series."
The first Ashes Test begins at Trent Bridge on Wednesday morning.