The goalkeeper's present contract expires at the end of the season.
Dawson, who has started the last two Championship fixtures after Keiren Westwood suffered a minor shoulder injury following their 2-1 defeat at leaders West Bromwich Albion, told The Star: "I just love playing football and that's me.
"I love the chance to walk out at Hillsborough and go away from home. I love being out there with the boys and that's all I am really concentrating on at the minute.
"I am quite easy about everything. I will just carry on doing my job and if I can stay in the team then that will be great."
As The Star exclusively revealed last month, a number of Championship clubs are keeping close tabs on Dawson's situation.
Derby County, Blackburn Rovers, Preston North End are big admirers of the 24-year-old. Dawson, a graduate of the Owls' youth system, is also believed to be on the radar of Scottish giants Rangers.
When asked about the possibility of extending his Hillsborough stay, Dawson said: "This is my club.
"I have been a bit unfortunate in that I have never seen the good days with this club. When I was growing up, it was the tough days of League One and scratching around in the Championship.
"I would love to be part of this club when we do get there (the Premier League). I want to really be part of it when there is a positive time for this football club."
Dawson was well marshalled by his defence in Saturday's 3-1 triumph at Charlton Athletic. There was nothing he could do about the Addicks equaliser, with Macauley Bonne's strike taking a wicked deflection off Tom Lees.
Even if Westwood has recovered from his knock, it is unlikely he will oust Dawson in between the sticks when the Owls entertain seventh-placed Brentford on Saturday.
As things stand, the number one spot looks like it is Dawson’s to lose.