Warriors announced in May that the Scotland centre was returning to the club after a season with Harlequins. Glasgow have since parted company with head coach Danny Wilson and it was reported in the Rugby Paper that Jones had had second thoughts about the move.
Stade Francais would have to pay a transfer fee to Glasgow for Jones but the Scotstoun club are confident the player is still intending to return north.
"From our point of view Huw has signed a contract and is coming to us," said a Glasgow Warriors spokesman.
Jones, 28, spent five seasons with Warriors before leaving last summer for Quins. He enjoyed a strong second half to the season and won a recall to the Scotland squad for the tour of South America but it was announced on Friday that he had withdrawn due to a back injury.
When the signing was announced, the 32-times capped Jones said: "I'm really looking forward to going back to Glasgow. I'm excited to return and show how I've developed as a player, and to pull on the Glasgow Warriors jersey again."
Glasgow are in the process of looking for a replacement for Wilson who was sacked after the 76-14 defeat by Leinster in the United Rugby Championship quarter-finals.
Dean Richards is the latest name to be linked with the vacancy. The former England and Lions forward is available after stepping down as director of rugby at Newcastle Falcons after ten years.
Richards, 58, is a hugely experienced coach having worked previously with Leicester, Grenoble and Harlequins. His involvement in the "bloodgate" scandal with Quins saw him banned for rugby for three years in 2009.
Todd Blackadder, the former Edinburgh captain, has also been reported as a candidate for Glasgow but it is understood he is not among the frontrunners.
A Glasgow spokesman said: We're still at the beginning stages of the process with a variety of candidates and a variety of scenarios."