The pair are entering the final year of their current deals and the club appear to be keen to tie them down to new long-term contracts.
Winger Dyer, who joined the Swans in 2009 from Southampton, has said that he hopes negotiations will be concluded shortly.
"The club is talking to my representatives at the moment," Dyer told the club's official website.
"If the deal is right then I'd love to sign a new contract - there's no doubt about that.
"My career has really developed here at Swansea and the manager (Brendan Rodgers) has really helped me a lot.
Teammate Allen added: "We are close to an agreement. There are a couple of little things that need sorting, but hopefully everything will be sorted soon.
Midfielder Allen made 43 appearances for the Swans last season, scoring two goals.