On the first Monday since the start of MLB free agency, the free agent pitcher was tendered a qualifying offer of a one-year, $17.8 million contract.
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Under MLB rules, the offer is the "mean salary of the sport's 125 highest-paid players." Cole has 10 days to accept or decline the qualifying offer.
Cole is likely to reject the offer, but the Astros made the move in the event he doesn't return. If he's signed elsewhere, Houston would receive a draft pick from Cole's new team as compensation.
In addition, the Astros can continue to negotiate on a long-term deal with Cole.
Cole made $13.5 million in the past season in Houston. He could command a long-term contract north of $200 million, according to some analysts.
Cole was one of eight players to file for free agency.
Also on Monday, starting pitcher Lance McCullers Jr., who was kept off the roster for the entire 2019 season after Tommy John surgery, was reinstated from the injured list.
Other moves by the Astros Monday include selecting minor league pitcher Kent Emanuel to its 40-man roster and declining the 2020 option on relief hurler Chris Devenski.
Brewery promises Gerrit Cole to keep his fridge full of beers if he stays