Mbabu made 31 appearances in all competitions for Die Wolfe in the 2021/22 season, laying on one assist.
Wolfsburg finished the Bundesliga season in 12th place with the same points tally as Eintracht Frankfurt, who qualified for the next edition of the Champions League as Europa League winners.
Mbabu previously was on the books at Newcastle United from January 2013 to the summer of 2017 but made only five appearances for them in all competitions, all of them coming in the 2015/16 season, sandwiched between loan spells with Rangers and Young Boys.
With primary target Neco Williams currently priced out of their range, the search for alternatives has led the Cottagers to Mbabu, who is eager to return and make an impression in the Premier League, according to Italy-based journalist Ekrem Konur.
The 27-year-old defender’s loan to Young Boys was made permanent in the summer of 2017, ending his association with the Magpies.
Fulham are looking to take advantage of his desire to return to the Premier League as the Swiss international has only a year remaining on his current contract with Die Wolfe.
Mbabu has played in the Champions League for both Young Boys and Wolfsburg, as recently as the last season in the group stage.