The attacking midfielder, who joined on loan from Real Madrid, came off the bench against Aston Villa last week and looked bright during his 25-minute cameo.
Odegaard will, as a result, be hoping to start against Leeds on Sunday and he could take the place of Emile Smith Rowe – particularly as Arsenal face Benfica in the Europa League on Thursday.
Captain Pierre-Emerick Aubameyang is also pushing to start against Leeds and could come in for Cedric Soares, with Bukayo Saka dropping into left-back and Nicolas Pepe switching from the left to right flank.
Alternatively, Mikel Arteta may opt to play Aubameyang as a central striker – in which case Alexandre Lacazette’s place looks under threat.
Arsenal will definitely have to cope without Kieran Tierney and Thomas Partey, who are out injured.
Goalkeeper Bernd Leno and defender David Luiz are, however, available again after returning from suspension.
Arsenal predicted lineup: (4-2-3-1) Leno; Bellerin, Holding, Mari, Saka; Ceballos, Xhaka; Pepe, Odegaard, Aubemayang; Lacazette.
Sunday 4.30pm GMT, BT Sport
Arsenal squad from: Leno, Runarsson, Ryan, Bellerin, Chambers, Gabriel, Holding, Luiz, Mari, Cedric, Ceballos, Elneny, Xhaka, Saka, Odegaard, Smith Rowe, Willian, Aubameyang, Lacazette, Nketiah, Martinelli, Balogun.
Injuries: Thomas Partey (hamstring), Kieran Tierney (lower leg)