I could assume that Fritz David Carlson (1888–-1952) was at least his informal advisor, although Carlson was a Swedish mathematician. Note that he is not represented in the Mathematics Genealogy Project.

Selberg's first contribution to the Polya-Gelfond problem was very close in style to Carlson's famous theorem (see, for example, [P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral, Trans. Amer. Math. Soc. 45 (2008) 489--534]).

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. $\ddot\smile$

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I could assume that Fritz David Carlson (1888–-1952) was at least his informal advisor, although Carlson was a Swedish mathematician. Note that he is not represented in the Mathematics Genealogy Project.

Selberg's first contribution to the Polya-Gelfond problem was very close in style to Carlson's famous theorem (see, for example, [P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral, Trans. Amer. Math. Soc. 45 (2008) 489--534]