The Texas Rangers and Los Angeles Dodgers are locked in a bidding war for free-agent right-hander Zack Greinke, and their back and forth has reached record heights, reports Jon Heyman of CBS Sports:

The Zack Greinke derby is currently between the Dodgers and Rangers, with a great likelihood that one of those teams will win the services of the top free-agent pitcher in the market, people close to the situation say...

The bidding is said by major-league officials to be "quite high'' now, with two people pegging the dollar amount at about $160 million. And that's with the deal not done yet...

Some have suggested they could even see the Greinke deal reaching toward the $175-million mark.

The current record for a contract given to a pitcher is the $161 million deal CC Sabathia signed when he re-negotiated with the New York Yankees following the 2008 season.

The Rangers are also in pursuit of outfielder Josh Hamilton, and may still be looking for a way to acquire Justin Upton from the Diamondbacks, so the team's interest in Greinke could shift significantly if it is able to acquire one of the other players.

The Dodgers, on the other hand, appear to be all in on Greinke and are thought by many to be the favorites to sign the right-hander.