Insiders say the agency has been told that the business is set to move in March 2006.
Meanwhile, Morgan Stanley has started contacting agencies with a view to drawing up a longlist to compete for its credit card and loans direct business. However, a brief has yet to be issued.
Tequila\ won the business in February after a pitch against Tullo Marshall Warren.
Morgan Stanley is one of the largest DM advertisers in the UK. In the past, the company has run campaigns throughout the year, rather than earmarking specific periods of activity.
It favours direct mail, which accounted for around £18 million of its annual UK direct marketing spend in 2004.
Morgan Stanley entered the UK credit-card market in 1999 with a £10 million launch. WWAV Rapp Collins handled the DM.
Morgan Stanley declined to comment on the forthcoming review.