Swans wait on Hylton
Hylton is available on a free transfer after Aston Villa opted not to renew his contract and The Swans want to tie up a permanent deal for the 20-year-old.
The left back impressed during a loan spell at Vetch Field last season and Swans director of football Flynn is eager to add Hylton to his ranks for next season.
Flynn has been in protracted negotiations with Hylton about bringing the youngster to South Wales permanently.
But Hylton's commitments with the England Under-20 squad have prevented the promising defender from resolving his future.
Hylton will be representing England in the Toulon tournament in France this week and Flynn is concerned a bold display from the left back will kibosh his chances of wrapping up the deal.
"Talks have been very productive," Flynn told the club's official website. "I met Leon this morning (Monday) for the second time and I'd say that we're very close to agreeing terms.
"He is keen on returning to Swansea on a permanent basis, he knows what we're about and I'd like to think that when he gets back from France we will be able to shake hands on it very quickly.
"Obviously we want him to do well but there's always a chance that other clubs might be alerted to him if he has a good tournament.
"That is why I was keen to get him signed before he went but that's not been possible."