Danish business paper, Borsen, said a number of senior investors in the company want Carlsen to be replaced with Vestas board member and FLSmidth chief executive Jorgen Huno.
The paper said last week's profit warning, which is the second in consecutive quarters, had motivated the investors to seek the replacement of Carlsen.
One anonymous source said: "Vestas knows well that we want a change in the chairmanship. There is also a natural expiry date for the chairmanship."
Last week, Vestas announced that it hoped to only break even for 2011, down from the €250 million profit predicted by the firm in October 2011. Previously Vestas had predicted a 7% profit margin for 2011 equalling €490 million.
It said the profit warning was largely caused by €125 million development costs of €125 million for the V112-3.0MW turbine.
The reports come as Vestas prepares to announce the details of a global restructure this week.