Henson was dismissed by the RaboDirect PRO12 outfit following an alcohol-related incident on a flight back from Glasgow and has since been linked with a host of sides in Wales, England and overseas.
The 30-year-old spoke to London Welsh earlier this season but their recently-confirmed promotion to the Aviva Premiership means a move to the Exiles is now more likely.
"We haven't spoken to Gavin since much earlier in the year, but we are obviously very much in the market for players of proven quality," said London Welsh managing director and 1971 Lion John Taylor.
"Gavin Henson has proved himself to be that time and time again. It is certainly possible that we will be back in touch.
"But, in that event, London Welsh would need assurances from Gavin that he is prepared to buy into our team ethic, our pay scales and that we would not just be a base for his other careers."
The Premiership's newest side are led by Henson's former Ospreys coach, Lyn Jones - a man who seemed to be able to get the best out of the double Grand Slam winner during his time in Swansea.
Henson won two Magners League titles, an Anglo-Welsh Cup, the majority of his 33 Wales caps and his solitary Lions Test cap while Jones was in charge at the Liberty Stadium.
Jones has often spoken of his admiration for the utility back, describing him as 'as influential as any rugby player in the British Isles' and sticking up for his former protégé after his sacking by the Blues.
But while Jones remains a huge fan of Henson's, he admits finances could prevent him from turning out at the Kassam Stadium next season.
"I really don't know what Gav's plans are. I haven't been in touch with him recently," said Jones.
"I'm sure that whatever he chooses to do, there will be a lot of money on the table for Gavin.
"Even though we have been promoted, and have huge resources available to us, we will still be working to a tight budget.
"As such, I don't know if we would be able to afford Gavin, or not. We will have to see."