Monk - the youngest manager in the league - signed a three-year contract last May when he was appointed on a full-time basis having succeeded Michael Laudrup in an interim capacity the previous February.
But the club are keen to reward Monk for his work in taking Swansea to their highest Premier League finish which has them in the running for Europa League qualification while warding off potential interest from rivals.
"I've began preliminary talks with the chairman and the club and I'm looking for the future to be with Swansea and progress it again for the following season," Monk said ahead of Sunday's league visit from Manchester City.
"I've had this opportunity to do this job for a great club and I love being here.
"I've been here for 11 years (as player and now manager) and doing this job really makes you appreciate that you're doing it for the fans.
"The responsibility is much greater but I've enjoyed every single minute of it."
Eighth-placed Swansea have compiled their best Premier League points haul under Monk and could yet climb into the top six with two rounds of matches remaining.
Arsenal boss Arsene Wenger and Crystal Palace Alan Pardew think it is an achievement worthy of winning the manager of the year award and Monk has already been linked to the Sunderland and West Ham jobs.
But the 36-year-old former Swansea captain expects talks designed to keep him at the Liberty Stadium will be stepped up over the next few weeks.
"We'll sit down and go into detail in the near future, whether that's in the next few days or weeks we'll see," Monk said.
"It's just a busy period at the moment to sit down face to face with my agent and the club
It's just getting everyone in the right place at the right time to discuss it.
"We only started to speak at the end of last week, just to say 'let's find a time to sit down and discuss it'.
"I am very focused on Swansea but it can take time on both sides to find an agreement.
"I am ambitious but I have no plans any time soon for that (being at Swansea) to be changing, but who knows in the future what happens?
"You either do well and possibly move on or you don't do well and you get sacked.
"In football it changes very quickly and you are always mindful of that as a player or manager."
Swansea are one point behind Southampton and two adrift of Tottenham and could yet play in Europe next season for the second time in three seasons.
Seventh spot would be enough to qualify for the Europa League should Arsenal beat Aston Villa in the FA Cup final on May 30.
"Hopefully in the long term I can achieve what I want to here," Monk said.
"We're pushing for Europe now - it's a real possibility - and that's a fantastic achievement where I'm at in my career now and for the players and the club itself.
"If we can achieve that it would be another stepping stone for the club."
Source : PA
Source: PA