The 21-year-old has spent an extended spell on trial at Wetherby Road this summer, featuring in pre-season fixtures against Newcastle United Under-23s, Rotherham United and Sunderland.
But Sulphurites boss Simon Weaver who wants to add another wideman to his squad ahead of the club’s second season in the Football League, has opted against making a move to sign Stevens.
"We have decided not to take Jordan," the Town boss told the Harrogate Advertiser.
"He's a good lad and a very talented footballer, but he's not the right fit in terms of what we need at this moment in time.
"The left wing is still an area we need to strengthen but we're looking for that Jack Diamond-type player, someone with real power who will drive at defenders down that side of the field."
Stevens, who spent time on loan with Swindon Town and Bradford City last term, featured five times under Leeds chief Marcelo Bielsa in the Championship, but has found his opportunities limited since the Whites were promoted back to Premier League.