Wing-back Stevens made his international debut in June against the USA, and hopes to have done enough to earn a call-up for Martin O'Neill's men when they face Wales in Cardiff next month.
But the former Portsmouth man insists that performances for Chris Wilder's Blades remain his No.1 priority, rather than focusing on more Ireland caps.
"I'm sure playing well in the Championship will help my international ambitions, but my aim is just to play well for United," Stevens said.
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"If I do well, and we do well as a team, then I will be rewarded off the pitch on the international scene.
"I have to keep my head down, keep focused. If I get the nod when September comes, I have to work hard then to break into the team."
Stevens, who has scored once in his United career, is hoping to accelerate the process somewhat by adding goals to his game.
"Definitely," he said when asked on the subject ahead of this weekend's Championship clash at Bolton Wanderers.
"It is one thing that the gaffer [Wilder] has said I should be doing a lot more of; getting into the box and getting on the end of crosses.
"It is something I am looking at and it is something I will hopefully improve on."