The duo were the subject of injury concerns following the team's 1-0 win over Burnley in the Premier League.
Partey, who started the game against Burnley, came off with a limp in the second period.
In his post-match press conference, Arteta said: "He struggled at the end. He was cramping but that will come because he's missed a long time. He needs some fitness back."
Tirney also came off in the game with an injury issue.
"Again he had a problem", Arteta added.
"I think he was cramping. The pitch was pretty difficult today it was quite long."
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