The 35-year-old former Arsenal, Tottenham and Portsmouth defender is a free agent after playing one game for Notts County during an ill-fated spell at Meadow Lane earlier this season.
Campbell has also been linked with moves to Newcastle United and West Bromwich Albion recently.
Rio Ferdinand, Nemanja Vidic, Jonny Evans, John O'Shea and Wes Brown are all currently sidelined although Serbia international Vidic is expected to be fit enough to play against Aston Villa this weekend.
Ferguson was forced to play midfielders Michael Carrick and Darren Fletcher as makeshift central defenders in Tuesday's Champions League victory at Wolfsburg.
The veteran manager said of Vidic: "I expect Nemanja to be fit for the Villa game and, if he's available, we'd have him and Michael Carrick, plus Darren Fletcher and Patrice Evra. I'd be happy enough with that."
Ferguson also expects to have Ryan Giggs, Wayne Rooney and Dimitar Berbatov available to face Martin O'Neill's team.
Source: DSG
