Crespo joined from Burberry in 2006. His move coincides with the retailer denying it is up for sale.
In a letter sent to staff seen by Retail Week, the management has said that the business, which is owned by property group Marylebone Warwick Balfour (MWB), has not been and is not up for sale.
However, last week, MWB released a stock exchange announcement that said it had extended the deadline for a sale of the group’s operational businesses, which include Liberty, until 2010 because of poor market conditions.
MWB took control of Liberty in 2000 with plans to turn the retailer around.
Last month, Liberty reported total group revenue increased to£45.8 million in the year to December 31 from£44 million the year before. However, pre-tax losses rose to£3.6 million as a result of increased investment in its Liberty of London brand.
A Liberty spokesman said a potential sale could involve a redistribution of shares among existing investors and not necessarily a trade sale.