The Jamaican sprinter, 31, could play a training match against Norway Under-19s next week, VG reports.
Bolt, who is the world record holder for the 100 and 200 metres, has previously trained with German Bundesliga giants Borussia Dortmund, South African club Mamelodi Sundowns.
The athletics legend said that he took football seriously and even suggested he could see himself playing permanently in Norway, he told VG.
“It's a country I generally enjoy. You never know what can happen, I just want to play football and prove for myself that I'm good enough,” he said.
“I'm just trying to improve. Maybe a club will see something and decide to give me a chance. So I'm going to keep working hard and maybe in future someone will offer something I can say ‘yes' to,” Bolt is quoted as saying by the Norwegian newspaper.
“I'm here to get in shape. I'm glad the club let me come and train here,” he told VG.
“It's a high tempo, and that's good,” he added.
Strømsgodset's sporting director Jostein Flo, a former Norwegian international, said that the club's first team players had been unaware the Olympic sprinter would be joining them for training.
“We said that a triallist would be joining us for training, and that he was up for it. Then the door was opened and Bolt came in. It was a shock for the players. They couldn't believe it,” Flo said.
With regard to next week's friendly against the national side's Under-19s, Flo said Bolt could be involved if he “stays here that long and is selected for the squad”.
Both Bolt and Strømsgodset are sponsored by German sports equipment manufacturers Puma, whose CEO is Bjørn Gulden, a Norwegian and former professional footballer with clubs including Strømsgodset and German side 1. FC Nürnberg.
Flo suggested that Bolt's arrival for training was more than just a PR stunt.
“We think it's fantastic that Usain Bolt is choosing to come here to Strømsgodset to train. He's one of a kind and a champion, one of the greatest athletes of all time, and we can clearly learn a lot from him,” Flo told Strømgodset's official website.
“His presence here will undoubtedly be a huge inspiration for players, coaches, the entire club,” he added.