Jones broke a bone in his shoulder in his country's win over Scotland on March 9 and looked to have possibly played his final game of the season.
The 32-year-old, who missed Wales Championship-clinching victory against England as a result, was expected to be sidelined for eight weeks but he insists his recovery is ahead of schedule and that he could be featuring for the Ospreys as early as the week after next.
"It's terrific news and I'm obviously delighted," Jones told the Telegraph Sport.
"I'm back running and doing some weights and a month down the line from that dreadful day at Murrayfield things are looking good.
"Ideally, I would be looking to play over the weekend of April 27 and 28 but, unfortunately, it's the Heineken Cup semi-finals and we are not in it. Because of that, I have thought about aiming for the weekend before against Glasgow.
"I've got an outside chance but I won't rush things if it's not the right thing to do. If not, I will certainly be there for the game against Leinster over the first weekend in May."
Jones won three Test caps for the Lions back in 2005 and was one of the stars of the trip to New Zealand after being called up to replace the injured Simon Taylor.
He missed out on initial selection in 2009 despite being captain of Wales at the time but his stock was again on the rise prior to his latest injury setback.
The back row cum second row was one of his nation's leading performers this spring and had taken over the captaincy once more prior to his heartache in Edinburgh.
His fine form on the international stage, together with his ability to play No4, 5, 6 or 8 and his obvious leadership qualities, led to loud calls for a Lions place and Jones admits selection is a key goal of his.
"I know that players are reluctant to speak of the Lions, especially when they are caught up in a busy Six Nations season. However, it's always there in the back of your mind and I'm certainly no different to anyone else," added Jones, who claims the prospect of a Lions place has aided the speed of his recovery.
"I have thought about it since the beginning of the season and I'm still thinking about it now.
"I suppose the news that I've had this week helps, because now I've got an opportunity that I didn't believe I would have.
"When you have the possibility of something like a Lions tour to aim for, you probably work that bit harder. That has certainly been the case for me.
"Having been on one before and having missed out on the chance in South Africa four years ago because of injury, I didn't want to come to the end of the season and thought, 'I could have worked harder'.
"If I make the tour, it will be a wonderful moment in my career. If I don't and it's down to the fact that I'm not deemed good enough, then I will accept that. But I didn't ever want to say to anyone, 'I'm not fit enough to go'."