(Reuters) - Liberty Media Corp Chief Executive Greg Maffei made an offer to buy internet radio company Pandora Media Inc in recent months, valuing the company at more than $3.4 billion, the Wall Street Journal reported on Thursday.

Pandora's board rebuffed the advance, because it believed the company's true value was closer to what it was in the fall, when the shares were trading around $20, the Journal said, citing people familiar with the matter.

The $15 per share offer from Maffei was several dollars above where the shares were trading at the time, the Journal said. (http://on.wsj.com/29OrWVd)

The music streaming company has also shopped itself to other potential buyers including Apple Inc and Amazon.com Inc, the Journal said.

Corvex Management LP, a hedge fund run by Keith Meister, a protégé of activist investor Carl Icahn, disclosed a 9.9 percent stake in Pandora in May and urged the company to explore a sale.

Unlike other streaming services, which have negotiated deals with record labels to allow listeners to pick songs, Pandora has acted more like a radio station, playing songs that match a genre but not allowing customers to make selections.

Liberty could not be reached immediately for comment. Pandora declined to comment.

Pandora's shares fell 2.8 percent to close at $12.00.

(Reporting by Rishika Sadam in Bengaluru)