A report in Superdeporte claimed that the Barcelona duo failed to see eye-to-eye after Villa had grown unhappy at the diminutive Argentine's central role in the squad.
However, Messi gave no credence to such stories and stressed there is a harmonious atmosphere within the squad at Camp Nou.
"The most important thing is that the players know that what is said is a lie," Messi told reporters at a press conference. "Those things are not real.
"I do not have any problem with Villa and I am surprised at what has been said. I have a good relationship with him and with the rest of my team-mates."
One of the 23 players to make the shortlist for the shortlist for the 2011 Fifa Ballon d'Or award, Messi stated he is not obsessed with clinching the prestigious accolade.
"There is still a lot of time before the ceremony and I am not thinking about it," Messi added. "I am not sure if I will win it or not.
"Last season, I did not know it until the last moment."
The Argentina international also played down comparisons with other players, including Real Madrid's Cristiano Ronaldo, saying: "I do not compete with any player.
"My goal is that this season is the best one for me and Barca and that we win the biggest titles, but without getting into comparisons with anyone.
"Those are things made by people who are on the outside. What I am worried about is that my team are successful."
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