Stroman was apparently unsettled by the latest rumors based on his response on Twitter:
The 27-year-old is coming off the worst year of his career, producing just a 5.54 ERA and 4-9 record while injuries limited him to 19 starts.
Stroman dealt with a shoulder injury during the middle of the season, while a finger issue caused him to end the year early.
Despite his struggles, the right-hander has proved to be a front-line starter in the past, including in 2017 when he posted a 3.09 ERA in 201 innings. He finished eighth in the Cy Young voting while also earning the American League Gold Glove Award.
In his first four seasons in the majors, Stroman had a 37-25 win-loss record to go with a 3.61 ERA.
The Padres are attempting to buy low on the young pitcher, who still has two more years under team control before hitting free agency after the 2020 season.
San Diego has a deep farm system but reportedly won't include top prospects like Fernando Tatis Jr., MacKenzie Gore and Francisco Mejia, per Morosi.
Pitching prospects Michel Baez and Logan Allen could be the centerpieces of a potential trade.
Teams have had interest in Stroman all offseason, although Morosi reported in November that the Blue Jays didn't have any serious talks with anyone. The Padres will hope the latest discussions can continue to advance to complete a deal.