Sarries, who are currently on a pre-season tour of South Africa and are due to play a Western Province Invitational XV on Friday, are hoping to follow fellow Guinness Premiership side Leicester Tigers in facing the world champions on their autumn tour of the UK and Ireland.
"We are in discussions with them [South Africa] to play in November. We were approached by the people representing the Wallabies and we've been approached by people representing South Africa," Saracens chief executive Edward Griffiths told the Hillingdon Times.
"I think the international teams have realised the way they play Test matches on weekends that a slightly larger squad can create revenue stream by playing mid-week matches."
The Springboks, who beat the Lions 2-1 earlier this summer, are already scheduled to play Test matches against France in Toulouse on Friday, November 13, Italy in Florence on Saturday, November 21 and Ireland in Dublin on Saturday, November 28, as well as a mid-week game against English champions Leicester at Welford Road.
Adding a fixture against Saracens would see the tour become more like a tour of old rather than the short, three or four-Test tours often seen in the modern era.
And while that in itself would present a new challenge to the Springboks, fitting the match into an already packed domestic and European schedule would also require some adaptation from Saracens themselves.
"It is a challenge because it would mean playing a weekend match and having to move a European or Anglo-Welsh match to play on a Friday and maybe playing on the following Tuesday. So it would mean playing three matches in a week which is a challenge," added Griffiths.
"We think we have a large enough squad to do that. There is no first XV, it's not a question of a reserve side. We have got two equal-strength sides.
"It definitely won't be at Craven Cottage. Vicarage Road is a possibility and our friends at Wembley are also very keen to have us back as soon as possible. It's not an easy decision one way or the other."