Eriksson appeared to distance himself from claims he was about to take the post on Wednesday when he revealed he was considering an offer to extend his contract as Ivory Coast head coach.
That could pave the way for Bradley, who guided the USA to the second round of the World Cup this summer.
Johnson has been a regular part of Bradley's squad since he took over in 2006, although he decided to omit the 26-year-old from his final 23 for the World Cup.
The striker, who signed for Fulham in 2008, believes there are a lot of similarities between the two managers, which would make Bradley an ideal candidate for the post at SW6.
"Bob could do a good job at Fulham," said Johnson. "If you look at the statistics then it's plain to see that he has done a good job with the US. They did well in the World Cup, won their group and played really well and that's all down to him."
Source: PA
Source: PA