Wells featured heavily for the Terriers last season, scoring 10 goals in 47 appearances across all competitions to help the club win promotion to the Premier League for the first time.
However, Huddersfield have spent a combined fee of around £15m to sign strikers Steve Mounie and Laurent Depoitre already this summer, and Wagner confirmed that Wells is now surplus to requirements at the club.
"Everybody can see how high the quality is of the strikers we've brought in. There is Mounie, Depoitre and we still have Elias Kachunga and Collin Quaner who are able to play there," he told reporters.
"This isn't the best situation for Nahki and, of course, he is the name who is on the market – so we will listen if there is some serious interest in him."
Wells, who was Huddersfield's record signing when they brought him in from Bradford City, has just one year remaining on his contract.