Pineda first joined the Twins as a free agent in December 2017 and made his return from Tommy John surgery this past season, throwing 146 innings across 26 starts.
The 30-year-old emerged as a reliable member of the Twins' rotation with a 4.01 ERA and 8.6 K/9 over that stretch, but his year was cut short by a drug suspension in September. The remainder of that 60-game ban will keep him out of action for the first 39 contests of the 2020 campaign.
Pineda currently slots in as the No. 3 starter in Minnesota behind ace Jose Berrios and veteran Jake Odorizzi, who passed up an opportunity to test the free-agent market by accepting his $17.8-million qualifying offer.
Top prospect Brusdar Graterol should join Devin Smeltzer, Randy Dobnak, and Lewis Thorpe in a competition for the remaining rotation spots, but the Twins' reported interest in other free-agent starters suggests Minnesota could still look to make a marquee addition.
The Twins were thought to be targeting Zack Wheeler before the former Mets right-hander landed with the Phillies, and the club is reportedly among the "heaviest suitors" for longtime Giants ace Madison Bumgarner.