If he comes through the week unscathed, Jones will pack down against Glasgow in Saturday's Magners League clash to put himself in contention for Ireland's visit to the Millennium Stadium on March 12.
Jones established himself as one of the world's finest tightheads during the 2009 Lions tour of South Africa and featured in the first two Test matches before suffering a dislocated shoulder.
A fully-fit Jones would be the first name on Warren Gatland's team-sheet and a recall for the penultimate Six Nations clash would be a perfect early birthday present for the prop who turns 30 on March 8.
"It was pretty frustrating at the start, but the rehab has gone well and I'm looking to take my first full contact this week," said Jones.
"I'm a pretty quick healer and if everything goes well this week then I'll be back for the game against Glasgow a week ahead of schedule.
"That's all I'm focusing on at the moment and it might not happen if I get a bad reaction in training.
"I'm obviously keen to get back, but there's a lot of rugby to be played this year for both club and country.
"Let's just see how things go this week, hopefully I'll come through it and then be able to look forward to the next few steps."
Jones and fellow Lions Test prop Gethin Jenkins have missed Wales' Six Nations campaign through injury with Ospreys pair Paul James and Craig Mitchell holding up the scrum.
Though the Welsh scrum hasn't buckled, there is no doubt that the loss of the two Lions props has reduced Wales' forward power, and Gatland would be keen to reintroduce Jones.