The Ivory Coast international has been linked with Chelsea and Manchester City in recent weeks, but Sky Sports have claimed United are also in the running.
The 26-year-old was close to agreeing a deal with Barcelona last summer, but the transfer fell through after Nice upped the asking price.
The midfielder is said to have an unofficial €40 million release clause in his contract, but his move to the Nou Camp collapsed after Paris Saint-Germain indicated they would offer €10m more.
Seri’s current contract expires in the summer of 2019 and Nice are believed to want to cash in now rather than risk losing him for nothing.