There is no database ID for ad-hoc queries. You could try parsing the statement and figuring out which tables it uses and which DB those are in.

But then, what database should this be associated with?

USE master

SELECT * FROM db1.dbo.table1

Or this one

Use TempDB

SELECT *

Into NotTemp

FROM db1.dbo.table1 t1 inner join db2.dbo.table2 t2 on T1.SomeID = T2.SomeID

Edit: Or you might be able to parse it out of the query plan, if you're familiar with XML.