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Teams had until midnight to make arbitration offers to their former players who became free agents, and Toronto will receive two extra selections in June's amateur draft if the right-hander decides to sign with another team.
The Blue Jays declined to offer arbitration to catcher Gregg Zaun.
Burnett went 18-10 with a 4.07 ERA in 34 starts last season and led the American League with 231 strikeouts. He opted out of the final two seasons of his five-year contract, deciding to try free agency and forgo $24 million the Blue Jays would have owed him.
Toronto is hoping to re-sign Burnett but could face stiff competition from several teams, including AL East rivals Boston and the New York Yankees.
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