Richards did not appear in the Premier League for Swansea last season and spent three months on loan in the Championship with Crystal Palace.
He enjoyed the experience at Selhurst Park, but now wants to challenge Angel Rangel to be Swansea's first-choice right-back.
"I went on loan to gain experience and get some game-time so you can return and push for a spot in the team," the 22-year-old told the club's official website.
"Obviously Angel is going strong and doing very well, but I hope to be a part of things this season.
"I don't know if I will go out on loan again, but you never know what can happen during pre-season.
"Just look at Ben (Davies) - he was among the best players we had in pre-season last year, and he went on to have a great season. When Tayls got injured, Ben went straight in because he had a great pre-season and was fit, sharp and ready.
"That's what it is all about. You go into pre-season, get your fitness in and show the manager what you can do. Then it's up to the manager. So that's what I'm hoping to do."