According to the New York Times, EA has made several recent attempts to buy out Valve with the most recent offer being around $1 billion.
Valve has reportedly rejected the offers with the reasons being they are currently happy with their status as a small privately-owned company and EA not coming anywhere close to the actual value of the company which is estimated to be around $2.5 billion.
According to Gabe Newell, the company also thinks had a deal been reached, EA would just terminate the company in a couple of years while keeping the sole rights to all the IPs owned by Valve. Newell would rather have the company shut down than be bought out if the choice was ever to be realistically made. Gabe Newell has said: