The 28-year-old played the last of his 13 Tests in July 2012 against South Africa.
Bopara has played regularly for England in limited-overs matches since then, but the Essex man has said that he would like to make a return to the Test arena.
"I don't know where I stand right now, but I know I've got to get runs - it's a simple formula," Bopara told BBC Sport.
"If you keep putting results on the board, knocking at that door, eventually someone's going to open it."
Bopara is expected to feature against Australia in the current one-day international series, which continues at Old Trafford on Sunday.