Blues acting chairman Peter Pannu told the club's official website that McLeish's job is "safe", but the Scot has been told the board expect him to lead the team back to the top flight at the first attempt next season.
Pannu told bcfc.com: "The board regrets Sunday's result and subsequent relegation and feels that supporters, who have continued to back us magnificently, have been let down.
"The club can confirm that manager Alex McLeish's job is safe but that the board will expect him to lead the side back to the Barclays Premier League in the 2011-12 season."
Blues' two-season spell in the top flight came to an end with a 2-1 defeat at Tottenham - just three months after lifting the Carling Cup.
McLeish led Blues to promotion in his first full season and their ninth-place finish in 2009-2010 was their highest in the top flight.
But the statement makes it clear that regaining Premier League status in 2011-2012 is of paramount importance.
Pannu added: "The board will take stock of what went wrong this season despite Carson Yeung's promised injection of ?£40million in funds - not ?£80m as the media wrongly assumed.
"The board will closely discuss and implement appropriate procedures to ensure a speedy return to the top flight.
"Finally a word for our terrific supporters, who are no doubt feeling the pain like everyone else connected with the club.
"We thank you for your tremendous backing - something we are confident we will still have moving forward as we embark on looking to make an immediate return to the Barclays Premier League."
Source: PA
Source: PA