The Owls stopper is on a season-long loan with the Grecians, who are pushing for promotion, and has kept 16 clean sheets in 43 appearances in all competitions.
The 26-year-old claimed three shut-outs in March and saved a penalty in a match against Oldham Athletic – where his Owls teammate Alex Hunt is currently on loan – to help his temporary club move up to second in the table.
Dawson previously featured in goal regularly for Sheffield Wednesday in the Championship but fell out of favour last season.
He is under contact at Hillsborough until the end of the 2023/24 season, although his long-term future remains unclear.
With Joe Wildsmith – who has not played for the club since December – out of contract and current first-choice pick Bailey Peacock-Farrell set to return to parent club Burnley, Sheffield Wednesday could be set for a goalkeeper overhaul this summer.
Speaking about his future in February, Dawson told Devon Live: “There has been no discussion and I have not spoken to anyone. I signed on loan here for the season and that is the job I am here to do.
“I can’t speak highly enough of the fans and they have taken me in wonderfully and I love playing my football in front of them.”
Dawson is up against Ben Garrity of Port Vale, Northampton Town’s Mitch Pinnock and Ruel Sotiriou of Leyton Orient for the award.
The winner will be announced on Friday.