The talented winger has shot to superstardom after his exploits in the Norwegian league at such a tender age, and has attracted the interest of elite clubs around Europe.
According to Tuttosport, Roma director Walter Sabatini is trying to steal a march on the other clubs by securing a deal in January.
Odegaard is a self-confessed Liverpool fan, and the Reds as well as Juventus, are also vying for his signature.
Odegaard has three goals in 18 appearances for Strømsgodset this season.