Danielsson has so far applied for a total of 17 ambassador jobs, 15 of which have been filled by other applicants.
The Brussels job is of particular importance as Sweden prepares to assume the presidency of the EU in the second half of 2009.
Bildt is reputed to have made it clear that he does not consider Danielsson suitable to represent Sweden as an ambassador.
One of the reasons for Bildt’s reluctance can be traced to criticism of Danielsson’s handling of the tsunami catastrophe in December 2004.