Rival Betfred Super League clubs, including Warrington Wolves and Salford Red Devils, have been linked with the 17-year-old who is rated as one of the country’s most promising young prospects.
Walker has scored five tries in six senior appearances this season, including a touchdown in each of Rhinos’ last two Super League games.
Confirmation from Rhinos he has rejected their contract offer opens the way for another club to step in.
In a statement released by Leeds, the Oulton Raiders product said: “At the moment I still want to keep my options open on my future.
“Leeds have been great with me in every department and the fans are unbelievable and I’m enjoying playing for this great club.
“The offer I’ve received from the club is fantastic, but it doesn’t come down to money. It’s the opportunity to play at full-back, a position I feel brings the best out in me.
“The club has a great young full-back in Ashton Golding, who is only two years older than me and who recently signed a four-year deal, so I need to look at my future and make the right call on my career going forward.”
Rhinos chief executive Gary Hetherington said Walker’s decision not to accept a promotion into the first-team squad is unique and insisted Leeds have made strenuous efforts to keep him.
“We offered Jack a full-time contract two months ago when he completed his studies at Leeds City College,” he said.
“We revisited it again last week because the lack of a commitment from Jack was becoming an issue within the squad and also affecting our planning for the future. This is obviously disappointing for us and unusual too as I cannot think of any other player to turn down a promotion to the Rhinos first-team squad from our Academy during my time at the club.
“Several of our senior players have spoken with Jack and I have personally met with him, his girlfriend and family to discuss the matter.
“However, Jack has made it clear that he wishes to only be considered for one position and has requested assurances that are never given to any player, irrespective of age and ability.”
Walker has been named in an under-strength initial 19 for tomorrow’s final game of the regular Super League season at Wigan Warriors.
Coach Brian McDermott said: “As a club we have a proud record for over 20 years of developing and rewarding our young talented players.
“So much of our club is built on the foundation nurtured through our academy. We recently announced that two such players, Danny McGuire and Rob Burrow, will bring down the curtain on their Rhinos career after 15 glorious years.
“The nature of our sport has meant that some players have also left the club during that period to seek better terms for themselves at other clubs whether that is a starting position or financial reward.
“Clearly on each occasion that has been disappointing, but has enabled us to reward those who want to take the club forward and be successful at the Rhinos.”