Yahoo’s new chief executive, Scott Thompson, is reportedly preparing to overhaul the structure at the Internet giant, which could include thousands of layoffs.

That’s the latest report from All Things Digital’s Kara Swisher, who cites “multiple sources both inside and outside” the company.

The layoffs, the report said, will be targeted at Yahoo’s product teams, and the axe may also fall on the company’s public relations and research teams. Sources told Swisher that the effort is being led by Thompson, who was appointed as the company’s CEO in January.

There have been plenty of other changes at Yahoo, including a complete shake-up of the company’s board. In February, the firm announced that chairman Roy Bostock and three other members of the board are on their way out, following Yahoo founder Jerry Yang.

Rovi’s Alfred Amoroso and LiveOps’s Maynard Webb have been tapped to join the board, and the company is still looking for more members.With the changes, all of Yahoo’s directors will have joined the board after 2010.

Swisher also reported that Yahoo’s recent decision to threaten Facebook with legal action over unspecified patents is being driven by Thompson, who is said to be aggressive.

In a recent conference call, Thompson said that he is planning big changes and that the company would look at new revenue streams, but he didn’t go into specifics.

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