The 23-year-old has been one of Arsenal's standout performers this season and continued his fine form in the 4-0 win at West Brom on Saturday with a goal and an assist.
Tierney has previously captained Scotland and his former club Celtic, and Arteta is confident the left-back can one day wear the Arsenal armband.
Asked whether Tierney can become a future Arsenal captain, Arteta said: "I think he can be, because he has the respect and the admiration of every member of the staff and every player.
Alexandre Lacazette has also been key in Arsenal's recent revival, having scored five goals in their last four games including two in their 4-0 win at West Brom.
Asked whether new contract talks with Lacazette are underway, the Spaniard said: "No, we haven't talked about anything related to his contract.
"We will talk in the summer and make a decision on what is going to happen.