The Pirates' decision could come this week, according to Heyman.
Shelton, 49, has spent the last two seasons as the Twins bench coach. His responsibilities changed in 2019 under first year manager Rocco Baldelli, taking on more day-to-day duties and running spring training.
Shelton was a quality control coach for the Blue Jays in 2017, when new Pirates general manager Ben Cherington was their vice president of baseball operations. Before then, he was hitting coach for the Indians and Rays from 2005-2016. He was a manager in the Yankees farm system from 2000-2002.
He was a finalist for the Mets' manager job earlier this offseason.
Quatraro, 46, just spent his first season as the Rays bench coach after spending a season as their third base coach in 2018. He spent four seasons as the Indians hitting coach from 2014-2017. Before then, he was the Rays minor league hitting coordinator from 2010-2013, and spent four seasons as a minor league manager in their system.
Quatraro was a finalist for the Giants' managerial opening.
Both Shelton and Quatraro were both initially interviewed by former general manager Neal Huntington in October. The Pirates paused their search for a new manager when they fired Huntington, wanting their next general manager to make the hire.
The Pirates are the final team looking for a manager for 2020.