The Finnish international has been dropped to third choice by Villa boss David O'Leary this season, with Danish custodian Thomas Sorensen the current number one.
The former Rangers, Liverpool and Galatasaray manager targeted the Scandinavian as cover for American international Brad Friedel while regular number two Alan Kelly recovers from a knee operation.
However, The Premier League have deemed Rovers' case to sign a goalkeeper outside the transfer window as not being enough of an exception to allow it and have blocked their move for Enckelman.
"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."
Meanwhile, O'Leary has called on Villa striker Darius Vassell to begin realising his potential with the club.
The England hit-man has had an inconsistent run of form in recent times and the former Leeds United manager is waiting for Vassell's promise to bear fruit for the Midlands side.
"There is so much more to come from Darius," said O'Leary.
"We are still waiting for that."
