"Stephen is being treated daily and we will monitor his progress during the course of this week, he is unlikely to take part in any form of rugby or running activity until next week," said Davies.
"He is still not walking comfortably, he will be given intensive treatment for the next four days or so and will work in the pool.
"If all goes according to plan he will hopefully be fit to resume rugby related activity next week, but it is fair to say it will be a race against time."
Wing Shane Williams is targeting a comeback for his region to prove his fitness after suffering a similar injury to Jones in Wales last Millennium Stadium outing and he joins Dragons fly-half Ceri Sweeney and Jones on the 'hoping to be available' list.
"Shane has resumed light training and hopes to progress this with a view to being included for the coming Ospreys match," Davies said.
"Ceri doesn't have a game for the Dragons this weekend, but we will be putting him through his paces in the next few days to ascertain how far down the road he is in relation to his fitness for inclusion next week."
Ospreys lock Ian Evans is also set to return to action for his region after serving a ban.