The Pistons' intrigue with a deal centers on the opportunity to land a future Phoenix first-round pick, perhaps as soon as the 2020 NBA draft, league sources said.
Talks have gained traction, but there is no agreement in place, league sources said.
The teams are expected to talk again Tuesday.
The Suns are traveling to Detroit to play the Pistons on Wednesday.
Kennard has missed 22 consecutive games with bilateral knee tendinitis, but is expected to return this season. The Pistons are struggling to find assets that can get them a significant return, and Kennard represents that opportunity for Detroit.
Suns vice president of basketball operations Jeff Bower was part of a Detroit front office that drafted Kennard with the No. 12 pick in the 2017 NBA draft. Phoenix is believed to imagine Kennard in a significant sixth-man role playing 30-plus minutes a game.
Kennard, 23, was averaging a career-best 15.8 points on 40% 3-point shooting before the knee injury sidelined him prior to Christmas. There has been hope that Kennard could return post-All Star Break in February.
ESPN front office insider Bobby Marks contributed to this report.