McArthur joined Wigan from Hamilton four years ago and has started both of the club's Championship games so far this season, scoring a late equaliser in the opening day draw with Reading.
The Scotland international is wanted back in the Premier League, though, with promoted Burnley making their move last week.
Reports suggest Burnley offered £4million for the 26-year-old, but the bid was rejected by their fellow Lancashire club.
Rosler is happy with how Wigan have handled the approach and he is determined to keep hold of McArthur during the transfer window.
"We confirmed there was a bid in and we acted in an appropriate manner," said Rosler.
"We told not only Burnley but everyone else that the player is not for sale. That’s all I need to comment on."