Henson, who hasn't played since April 2009, is still under contract with the Ospreys but has made no secret of his desire to join a club in the London area this season.
The 2005 Test Lion is currently taking part in the BBC reality TV series Strictly Come Dancing but is desperate to rekindle his Wales career prior to the 2011 World Cup.
Sarries lost fly-half Derick Hougaard to a ruptured Achilles tendon last weekend and chief executive Edward Griffiths has admitted that he has already sounded Henson out about a possible move.
"It would be wrong to provide a commentary on negotiations with one individual, Griffiths told the Daily Telegraph.
"But I can confirm there has been contact between us and Gavin.
"We're looking at various players who could possibly come in and we're hoping to do something by the weekend," added Griffiths when talking to BBC Three Counties Radio.
"We are contemplating various options, one of those options might be to go with the players we have. Another option is to bring players in.
"We're reasonably well covered but we're just looking around and seeing if there are other players who could add something to the squad.
"It's not easy to find players of the required quality but we will cast our net wide and see what it brings."