The Wales back row cum second row broke a bone in his shoulder in his country's win over Scotland on March 9 and was initially ruled out for eight weeks.
Jones insisted earlier this month that he had a chance of returning earlier, though, and he subsequently targeted the key league encounter with the third-placed Scots as a possible comeback fixture.
"Ryan Jones won't be involved this weekend," said Ospreys assistant coach Gruff Rees.
"He's as per the target, which was always the Leinster away game (on May 3)."
With the Warriors fixture coming too soon and the Ospreys not in European action on the final weekend before the squad announcement, Jones will now have to hope that Lions coach Warren Gatland saw enough prior to his shoulder setback to secure his place on the plane.
Jones was a key figure in Wales' Championship triumph this spring, captaining his country to wins in Paris, Rome and Edinburgh before injury struck at Murrayfield.
The 32-year-old received plenty of praise from all quarters for his fine form and impressive leadership skills as Wales bounced back from the worst possible start to the campaign when they were beaten by Ireland in Cardiff.
But back row arguably appears the most competitive area when it comes to selection and Gatland, Rob Howley, Graham Rowntree and Andy Farrell have a huge array of talent to pick from.
History will give Jones mixed impressions of his chances as he missed out on initial selection for the tourists when Gatland was assistant coach to Sir Ian McGeechan four years ago, even though he was captain of Wales at the time.
He had also been overlooked in New Zealand in 2005 but went on to feature in all three Tests against the All Blacks after being called up as a replacement for Simon Taylor.
Despite his current unavailability, Rees is convinced that Jones deserves another shot with Britain and Ireland's elite and he is backing a whole host of his Ospreys squad to be on tour with him this summer.
"Ryan is Mr Consistent, but he also has a unique knack of turning good groups of players into great groups," added Rees.
"How many Ospreys would I take to Australia? Well, Wales won the Six Nations and you'd hope and expect that the starting XV against England could make it.
"There were six Ospreys that day and all of them have to be in serious contention, plus Ryan."