The Swans secured promotion into the Premier League last season with Dutch shot-stopper Dorus de Vries providing their last line of defence.
He has opted to move on this summer, penning a three-year contract with Wolves.
That has left Brendan Rodgers short on options, with last season's back-up Yves Ma-Kalambay now available as a free agent.
Swansea are hoping to tie him down on fresh terms, but appreciate that they need to bring in at least one more senior keeper.
"There are a few options we are looking at," Jenkins told the South Wales Evening Post.
"Goalkeeper is obviously a position we need to look at, and talks are ongoing. Hopefully something will develop in the next few days."
Reports suggest Fulham's Stockdale tops Rodgers' wish list, with the Cottagers having admitted that they would be willing to let the England squad member leave on loan.
Blackpool's Matt Gilks is also believed to be a target, with the Scotland international having allowed his contract at Bloomfield Road to run down.