Graham told the Alan Brazil Sports Breakfast: "I think he has got to take a look at his career and ask himself why he is not first choice every week for Arsenal."
The ex-Spurs and Leeds boss went on to say how players should focus on their club form first before even thinking about international duties.
“Never mind England!," he said. "I think there are a few players who have got to be more hungry and want to be a regular every week for Arsenal. Then, and only then, can they start talking about England.”
The former Southampton speedster has been a target for critics this season, following a succession of tepid displays, with his physical and mental prowess being called into question.
Following Arsenal's 3-2 defeat to Manchester United, his former England colleague Jermaine Jenas told BBC Radio 5 Live how he was amazed by Walcott's lack of influence on the Arsenal team:
"He's been there for 10 years and I'm thinking, you've been here for 10 years, what is your influence on this team? When you've been at a club for that long, you would expect to have more of an influence."
The Arsenal man's dip in form has coincided with him losing his starting role in the national side and he will have a lot of work to do to regain his place.
He will be hoping a late season surge can drive Arsenal on to Premier League glory, and in turn earn himself a starting berth at the Euros.
Walcott has scored just eight goals in 36 appearances this term for the Gunners, with the Arsenal management still seemingly unsure of his best position.