However, the 21-year-old has revealed that Jenkins had been tracking his progress since his time at Charlton Athletic, where he played for two years from 2008 to 2010.
"When I spoke to the Swansea chairman, he said they had been tracking me from my Charlton days. I also heard of a link when Joe Allen was going to Liverpool, but that never happened," Shelvey told reporters.
"It raised its head again over the summer and I was following it in the papers every morning while on holiday until it happened for real.
"Less than two hours after I had agreed to sign, people were coming up to me in the local Sainsbury's in Swansea for autographs and pictures."
Shelvey has already made his debut for Swansea, playing 45 minutes in a friendly against FC Gravenzande before another 45-minute stint against Excelsior.