The tourists finished 111-2 on the third day and must score a further 229 runs to secure victory, a total which would see England better their previous best effort of 332 set against Australia in 1928.
“I’d say it’s pretty 50/50 to be honest,” said Swann. “Obviously we’d like to be chasing a few less than we actually are, but having said that we’ve got off to a decent start finishing on 111-2.
“Jonathan Trott and Kevin Pietersen look good in the middle. So we’ll be hoping we can score 200 runs tomorrow and we’ve got eight wickets spare so it’s not an impossible task”.
England started the day needing five wickets to dismiss the home side but were made to wait until just before tea with the final two wickets adding 87 valuable runs.
Wicket-keeper Prasanna Jayawardene led the way with 61 not-out – his fourth Test fifty – delivering some lusty blows to drain England’s confidence.
However, England felt they had their man with the score at 168-5, but Jayawardene was reprieved after the Stuart Broad overstepped having taken a catch off his own bowling.
Despite the daunting task facing the remaining eight batsmen, the pitch remains true to those who occupy the crease, and Swann is confident England can pull off a historic run chase.
“It’s not at all [difficult conditions to bat],” added Swann.
“It’s still a very good deck. It’s very slow but the outfield is very quick so there’s boundaries to be scored and you can rotate the singles as well.
“I think a couple of the Sri Lanka guys showed with a bit of aptitude you can be very hard to budge,” added Swann.
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Anthony Martial