Price, 57, served as manager of the Cincinnati Reds for parts of five seasons (2014-18), posting a 279-387 (.419) record.
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Prior to his managerial stint with the Reds, he was the team's pitching coach for four years (2010-13).
Under Price's term as pitching coach, the Reds made the postseason three times (2010, 2012-13) in four seasons and right-hander Homer Bailey tossed two no-hitters.
Before his time in Cincinnati, he served as pitching coach for the Arizona Diamondbacks (2006-09) and Seattle Mariners (2000-05).
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Also, in 2009, he spent part of the year working for the Phillies as a minor league pitching consultant.
An eighth-round selection by the California Angels in the June 1984 draft, Price went 31-19 with a 3.74 ERA in 90 minor league games (75 starts).
Last week, the Phillies announced Joe Girardi as their new manager.