Bassey travelled to Morocco at the beginning of the international break to link up with his Nigerian teammates ahead of friendlies against Ghana and Mali.
However, the former Rangers centre-back was unable to feature in last Friday's 2-1 win over Ghana due to an injury issue.
After being ruled out of the 2-0 defeat to Mali, the 24-year-old returned to Fulham's training base to work on his recovery.
Despite the obvious concern surrounding Bassey's fitness, the Evening Standard are reporting that he should be available for the upcoming trip to Bramall Lane.
The report claims that early assessments suggest the injury is not as bad as originally feared, providing Marco Silva with a boost ahead of the weekend.
After returning from the Africa Cup of Nations in February, Bassey enjoyed a run of four consecutive starts prior to the international break.
Those run of games began with a narrow 2-1 victory against Manchester United at Old Trafford, where Bassey opened the scoring with his first goal for the club.
Having started 16 of his 20 league appearances this season, the Nigerian is poised to line up in central defence alongside Tosin Adarabioyo on Saturday.
Do Fulham have any other fitness concerns?
With Bassey likely to be passed fit, Silva has indicated he could have a full squad available for an away clash against a struggling Sheffield United side.
"It looks like everything is going to be OK," Silva told reporters at Thursday's pre-match press conference. "We'll have to assess them on Friday again and take decisions, but no serious problems."
Fulham are currently enjoying a promising run of form, having won three of their last four matches, including a 3-0 victory over Tottenham Hotspur in their most recent outing.
While they may be sitting in the bottom half of the table, the West London club are just four points adrift of eighth place, which could become a European qualification spot by the end of the season.