The pair, who have struggled with injuries this season, were on the bench for last week’s 4-0 defeat to Liverpool.
Tierney could come into the side for fellow left-back Nuno Tavares, while Odegaard may replace Alexandre Lacazette in the No10 role.
Mikel Arteta also has a decision to make in midfield given Albert Sambi Lokonga struggled to perform at Anfield.
Ainsley Maitland-Niles could come in for the Belgian, while Mohamed Elneny is another possible starter.
Arsenal are looking to get back to winning ways against Newcastle as defeat to Liverpool ended their 10-game unbeaten run.
Arsenal likely XI (4-2-3-1): Ramsdale; Tomiyasu, White, Gabriel, Tierney; Partey, Maitland-Niles; Saka, Odegaard, Smith Rowe; Aubameyang.
Saturday 12.30pm GMT, BT Sport
Arsenal squad from: Leno, Ramsdale, Okonkwo; Cedric, Chambers, Gabriel, Holding, Mari, Tavares, Tierney, Tomiyasu, White; Elneny, Lokonga, Maitland-Niles, Odegaard, Partey, Saka, Smith Rowe; Aubameyang, Balogun, Lacazette, Martinelli, Nketiah and Pepe.
Injured: Kolasinac (ankle) and Xhaka (knee).