Rovers were hoping to be given permission to sign Enckelman on loan outside of the transfer window as cover for Brad Friedel while Alan Kelly recovers from knee surgery.
However, the idea has been dashed by the Premier League.
"We made an enquiry to the Premier League about bringing in a keeper because there's a special dispensation for goalkeepers but we were told 'no'," Rovers chief executive John Williams told the Lancashire Evening Telegraph.
"So unless we get an injury to either Brad or David, which we obviously don't want, then we won't be given permission."