Hodgson has been linked with the job since Lars Lagerbäck’s nine-year reign as Sweden manager ended on Wednesday following the team’s failure to qualify for the World Cup.
The 62-year-old began his managerial career with Swedish club Halmstad in 1976 and also had spells with Malmö and Örebro in the Swedish league.
He admitted he was flattered to be mentioned as a candidate but played down any suggestion he might be interested in leaving the Premier League club.
“I haven’t been contacted about the Sweden job,” Hodgson said. “I have a contract until the end of the year here so I’m not free to take a job until June or July.
“Firstly, as far as I know Sweden have always gone for Swedish coaches and I would be very surprised if they don’t go for another Swedish coach.
“And secondly I’m quite happy here so hopefully my time here will continue a bit longer.”
Hodgson confirmed he has not held any formal discussions with Fulham’s hierarchy about a new deal but he believes his future remains in west London.
“I would like to think the job that I have done here, and am doing here, is a good one,” he added.
“If a new contract offer comes up then I’ll consider it. Every week things change, your position is stronger and weaker week by week dependent on whether you have won a game or lost a game.”