I could assume that <a href="http://en.wikipedia.org/wiki/Fritz_Carlson">Fritz David Carlson</a> (1888–-1952) was at least his informal advisor, although Carlson was a Swedish mathematician. Note that he is not represented in the <a href="http://genealogy.math.ndsu.nodak.edu/">Mathematics Genealogy Project</a>.

Selberg's first contribution to the Polya-Gelfond problem was very close in style to Carlson's famous theorem (see, for example, 
<a href="http://www.maths.uq.edu.au/~uqowarna/pubs/Selberg_review.pdf">[P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral, *Trans. Amer. Math. Soc.* **45** (2008) 489--534]</a>).

**EDIT.** This was only my guess (as I indicate in my comments above to the question, I have believed that Selberg was self-educated). I asked the question Gert Almkvist, who knows a lot of Scandinavian math history. He answers:

> It is evident that Selberg had no
> advisor, but somebody had to sign the
> papers. Harald Bohr fled to Sweden
> when the Germans invaded Denmark. He
> was in Lund and Stockholm. But he did
> not dare to go to Oslo for the thesis
> defense.

Then Gert adds that he has a huge biography of Harald Bohr but this could serve for a different question. $\ddot\smile$