Buttner is understudy to first-choice left-back Patrice Evra though he still made 13 appearances last season as he won a Premier League winners medal in his first season at United.
Buttner was one of Sir Alex Ferguson's last signings. But new boss David Moyes is being linked with a raid on his former club Everton for England left-back Baines.
Frenchman Evra is not expected to leave even if Baines does arrive, and that would leave Buttner as the likely third choice left-back.
The Dutchman said: "The speculation doesn't bother me. I hear the name Baines but for me I don't care.
"I want to play my own game. If he comes I don't think my future will be in danger.
"I just want to be strong and let the trainer see what I have got. I don't think about other players, just myself."
Most United observers believe that Evra improved his performances following the arrival as Buttner, with the youngster providing him with genuine competition for a starting place.
"Manchester United need two good left-backs," said Buttner. "I put pressure on Patrice because I did well when I played.
"But Patrice did well also. That is the way it works at United, you put pressure on each other.
"I played 13 games for this team. That is good. This season my target is to play more games. I want to go for the left-back position."