The Wolves striker was linked with a switch to Elland Road after he was transfer listed by the Molineux club at the end of last season, but Wise is understood to have turned his attention towards other available forwards.
Johnson joined Leeds from Wolves in February but made only five appearances before returning to the Midlands after a final outing at Derby County on the last day of the 2006-07 season.
Wise revealed initially that he had signed Johnson on loan with a view to a permanent deal, but also stated he was anxious to assess the striker's attitude and temperament after an unsuccessful first season with Wolves.
The American moved to the West Midlands from Blackburn last summer but made little or no impact under boss Mick McCarthy.
United hoped to revive his career with a spell in West Yorkshire but Johnson struggled to make an impression and is now believed to have gone down the list of preferred options available to Wise.
Leeds are reluctant to part with any cash for the 22-year-old, and any agreement would certainly depend on Wolves giving him a free transfer or negotiating a part-exchange deal.
McCarthy is expected to want a fee for Johnson having prised him from Ewood Park only 10 months ago.
Johnson joined Leeds from Wolves in February but made only five appearances before returning to the Midlands after a final outing at Derby County on the last day of the 2006-07 season.
Wise revealed initially that he had signed Johnson on loan with a view to a permanent deal, but also stated he was anxious to assess the striker's attitude and temperament after an unsuccessful first season with Wolves.
The American moved to the West Midlands from Blackburn last summer but made little or no impact under boss Mick McCarthy.
United hoped to revive his career with a spell in West Yorkshire but Johnson struggled to make an impression and is now believed to have gone down the list of preferred options available to Wise.
Leeds are reluctant to part with any cash for the 22-year-old, and any agreement would certainly depend on Wolves giving him a free transfer or negotiating a part-exchange deal.
McCarthy is expected to want a fee for Johnson having prised him from Ewood Park only 10 months ago.