One variation of the deal includes the Dodgers taking pitcher Homer Bailey from the Reds and his $28 million remaining salary to buy Reds prospects.
"We've had conversations with the Dodgers, and there have been a variety of permutations," Reds president of baseball operations Dick Williams said, according to MLB.com. "I'm not going to get into what we've talked about."
Williams also said that none of those talks were close to getting a deal complete.
Puig, 28, hit .267 with 23 home runs and 63 RBIs in 125 games last season for the Dodgers. The 2014 All-Star selection hit a career-high 28 home runs in 152 games for the Dodgers in 2017. He made $9.2 million in 2018 and is eligible for arbitration in 2019. He can become a free agent in 2020.
Bailey, 32, was 1-14 last season with a 6.09 ERA in 20 games. He made $21 million in 2018 and is due $23 million in 2019. Bailey has a $25 million mutual option in 2020 with a $5 million buyout.