The 21-year-old scored twice in six appearances on loan for Town this season and manager John Gregory wants him back next term.
But Edwards, who was on target for Wales Under-21s as they lost 3-1 to England on Monday night, hopes to make the breakthrough at the Liberty Stadium.
"I would like to do pre-season at Swansea," he told the Swans' website. "This is my club and I would like to get a chance here.
"If I don't get a chance or the manager wants me to go out and get more games, I am happy to do that.
"I have been in and around first-team football this season which has been good for me because I'm 21 now.
"Getting games under my belt is the big thing for me now and hopefully I can get some more next season.
"I scored on my debut for Crawley which was good and there was talk of the manager wanting me back next season, but I will just see what happens."