The Barcelona ace has been voted the world's best player in two successive years and he is regarded as one of the greatest in history.
Rooney and Messi also went head-to-head in May's Champions League final, where both scored but the Argentine was one of the main reasons Barcelona cruised to a 3-1 win.
United striker Rooney realises he is not at the same level as Messi and he has set his sights on reaching the standards set by the 24-year-old.
Rooney said: "Messi is a great player and rightly World Player of the Year.
"For every footballer out there, not just me, that's the target you want to try to get to and, hopefully, I can.
"I want to do well all the time and know I can always improve.
"I work hard every day to try to achieve that so it'll be great for me and the club if I do."