The U's are searching for a new boss following the sacking of Pep Clotet on January 22 and the former Arsenal and Tottenham Hotspur defender has since held talks with the League One club about filling the vacancy.
Everton Under-23s chief David Unsworth had been considered the favourite to succeed Clotet at the Kassam Stadium, but it is now understood the 44-year-old is out of the running.
It means that Campbell could be given his first job in management after previously admitting on Soccer AM last month that he wanted to move into the dugout.
"I'm looking for a job in football, that's what it's all about. I want to manage," the 43-year-old said.
"I understand it's a difficult environment, even though I've got a top-notch CV, but I understand you've got to start from the bottom and work your way up.
"It's all about working towards my goal. Yes, you've got to start all over again, but it's all about building a new career and I'm willing to do that."
Campbell came through the youth ranks at Spurs and spent nine years in their first team before causing huge controversy in the summer of 2001 when the centre-back left them for fierce North London rivals the Gunners on a free transfer.
The former England international won two Premier League titles and four FA Cups after making the move, before stints with Portsmouth, Notts County and Newcastle United before retiring from playing in 2011.