The former Ospreys star is without a club having been dismissed by Cardiff Blues in April.
But the Exiles, who kick-off their Aviva Premiership season against Leicester Tigers on September 2, could offer the Grand Slam winner a chance to resurrect his career.
"I'll certainly be on the phone to Gavin to see if he is interested," said London Welsh head coach Lyn Jones.
"He used to be a very good rugby player, and if he has an appetite I'm sure he would be a very good addition."
The famous club are launching a major recruitment drive following their successful appeal to win promotion to the Premiership.
They have six to eight places in their squad available and will bid for the highest calibre of player.
Jones has previously worked with Henson during some of his best years, while at the Ospreys, and the Exiles approached the former British Lion in April.
Jones added: "Recruitment is an ongoing process and for us it's massive. We've got a few people that we're keeping our eye on but we need to spend our money wisely and they need to be the right players.
"We're not ruling anybody out. It's important that you recruit sensibly and Gavin will be one of the names we look at."
Henson has played for Saracens, Toulon and the Blues since leaving the Ospreys in 2010.
He earned an international recall in 2011 and was in contention to be named in Wales' World Cup squad. But he dislocated his wrist in the World Cup warm-up victory over England at the Millennium Stadium