Odegaard has been out since last month after suffering a knee injury in victory over West Ham.
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The midfielder missed Norway's World Cup qualifiers this past week, but The Sun says he is in line to make Sunday's derby.
Odegaard's return would offer a huge morale boost to manager Mikel Arteta and his Arsenal players.
However, Tottenham could also be set to receive a pre-match lift with Randal Kolo Muani in line for a recall. The France striker suffered a major jaw injury during the draw with Manchester United, with early claims he would miss two months.
But Muani is now on track to make Spurs' matchday squad this weekend.