Kennedy ended up surrendering just three runs in six innings while earning the win against the Cubs.
The 29-year-old has been floating around trade rumors for a while, especially as the Padres have been open to make deals. On Tuesday, they sent third baseman Chase Headley to the Yankees for infielder Yangervis Solarte.
The Yankees are familiar with Kennedy. He spent the first three years of his career with the team, going 1-4 before he was traded to Arizona, where he won 21 games in 2011.
New York’s general manager, Brian Cashman, has said he wants to make a deal before the July 31 trade deadline. But, on Wednesday, he said he’d prefer to add a piece on offense.