The England star missed Everton's win at Preston last night and Fulham hope to seal the deal in time for him to join up with his new team-mates when they return from their pre-season tour of Korea next week.
If the transfer goes through, Johnson would link up with another summer arrival - former West Ham striker Bobby Zamora - at Craven Cottage this season.
Bullard is keen to remain with Fulham but with Wigan willing to pay in the region of £5m for him, Hodgson will now consider the options.
Bullard signed for Fulham two years ago for £2.5m and has made just 20 starts due to a serious knee injury.
His return to fitness, however, played a crucial role in Fulham's improbable escape from relegation last season.