The 21-year-old Wales international made his debut against Blackpool at the end of the 2006/07 campaign and has gone on to become an integral part of Brendan Rodgers' side, turning in a number of impressive displays as they secured promotion last term.
Rodgers and chairman Huw Jenkins have made no secret of their desire to tie Allen to a long-term deal at the Liberty Stadium, and the player, who has a year left on his current contract, told the club website: "We are close to an agreement. There are a couple of little things that need sorting, but hopefully everything will be sorted soon."
Another man keen to stay in south Wales is Nathan Dyer. The former Southampton winger is also in the final year of his contract, and hopes that ongoing talks will see him commit to Swansea.
Dyer, who was named the Supporters' Player of the Year last term, said: "The club is talking to my representatives at the moment.
"If the deal is right for me 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 has really helped me a lot. I want to keep pushing myself and hope my ability will cause a few problems in the Premier League.
"It's a dream come true for me to play in the Premier League and, to be honest, it still hasn't really sunk in yet; it doesn't feel quite right.
"It hasn't hit us yet. I'm sure when we play Manchester City it will smack us in the face. But there is a good squad here at Swansea and we are all looking forward to it."
Swansea are also close to agreeing a one-year contract extension with Republic of Ireland international Thomas Butler. The 30-year-old midfielder missed all of last season with a thigh injury.
Source: PA
Source: PA