Delap is a free agent after his contract at the Britannia Stadium expired, and he admits he had contemplated bringing his career to an end after losing his place in the side.
However, a loan spell with Barnsley at the end of the season helped the 36-year-old rediscover his hunger for the game and he believes he still has something to offer.
The midfielder, who started his career with Carlisle United, insists he would have no problem playing for a club lower down the Football League.
"I just want to keep playing, at least another year," Delap told Sky Sports News.
"There were thoughts, to be honest, while I was still at Stoke that I might possibly have to leave it this season, but going to Barnsley I felt quite comfortable in the games I played in and that gave me a new impetus to play.
"Unfortunately I got an injury but that has cleared up now and hopefully someone will give me an opportunity to prove that I can play.
"I don't know what level that will be at. I felt good in the Championship and I have always said I don't mind dropping down the leagues.
"As long as I am playing, I am happy."