The newspaper cited three people familiar with the matter and said a deal could be announced as early as Tuesday morning. The report said the exact value of the purchase couldn't be learned but said its full value would likely be more than $20 billion. That would include an equity price greater than the company's market capitalization of $12.3 billion, along with the assumption of $6.3 billion in debt.
Archstone-Smith's CFO declined to comment on the matter Monday, according to the report.
Archstone-Smith's shares traded heavily Friday after an industry newsletter reported that the trust was in buyout talks. Shares ended the session up $4.10, or 8%, at $55.23.
U.S. stock markets were closed Monday in observance of Memorial Day.