The all-rounder has been included in the T20 squad to face Sri Lanka on 5 July at the Ageas Bowl, having been part of the World T20 squad in March.
"It's nice to be involved again," the 26-year-old slow left-armer and right-handed batsman told BBC Radio Solent.
"I wasn't expecting to be as I thought Moeen Ali would, but him being rested hands me another opportunity."
Dawson failed to make an appearance during England's run to the World T20 final in India this year, but his limited-overs performances for Hampshire this season have kept him in contention.
"I'm not sure what team they'll go with," he said.
"I've had some good performances for Hampshire in one-day and T20 cricket and if I keep going with that, hopefully I might get a chance."
Hampshire's Liam Dawson says it would be "amazing" to make his England Twenty20 debut on his home ground.