The Swans have already sealed the signature of Spanish midfielder Jose Canas, but they have reportedly had a bid turned down for Standard Liege's 19-year-old striker Michy Batshuayi.
Boosting their attacking options appears to be Michael Laudrup's top priority this summer, with Lyon striker Bafetimbi Gomis and Anderlecht's Dieumerci Mbokani also believed to be targets.
Swansea are now preparing for a Europa League campaign after their Capital One Cup triumph and Jenkins says that a number of deals are on-going.
"We are working day and night and there is a lot going on behind the scenes," he told the South Wales Evening Post.
"There are a lot of options and a lot of discussions have taken place.
"We have talked to many clubs, and in some cases we have put certain bids in for certain players. But some clubs prefer to wait to see what other offers come in.
"If you get as far as the dealing with the player or the agents, they are happy to sit and wait in some cases too. It's not just us finding that, it's the same for a lot of Premier League clubs."