(Adds TreeHouse statement) Feb 10 (Reuters) - Jana Partners is pushing TreeHouse Foods to explore options, including a sale, after taking a 7.3% stake, the hedge fund disclosed in a filing on Wednesday, sending the packaged food company’s shares up more than 19%. Jana bought more than 4 million shares in TreeHouse as it viewed the stock to be undervalued even after nearly three years into a turnaround, the hedge fund said. The fund also said it would propose three nominees for election to the company’s board. “TreeHouse is open to constructive input from all stockholders,” the company said in a statement. TreeHouse had a market capitalization of about $2.86 billion, with its shares closing at $50.69 on Wednesday. Jana continues to have "constructive discussions" with the board to resolve undervaluation and total stockholder return, including evaluating a sale, according to the filing here.