"Padres recently reaffirmed to other teams that they continue to be open for business," Olney tweeted on Wednesday, adding that Hand is the "primary guy on the table."
Hand has a 1.73 ERA in 22 games this season, striking out 35 batters over 26 innings.
According to Dennis Lin of the San Diego Union-Tribune, the Padres have had "very preliminary discussions" with other teams regarding Hand.
The 27-year-old, who appeared in a major-league high 82 games in 2016, is slated to make $1.375 million this year and is eligible for arbitration in 2018 at the earliest.
-- Alex Tekip