The Belgium international, 29, had another fine season in Serie A last time out.
Nainggolan netted 14 goals and chipped in with seven assists in all competitions for Roma.
And according to Italian outlet Calciomercato, Roma are under pressure to sell their star players to meet Financial Fair Play rules.
Mohamed Salah is expected to join Liverpool this summer, which could solve Roma's dilemma.
They reckon the Premier League giants are eying the midfield maestro with Champions League football returning to both clubs next season.
Roma want around £44m (€50m) for the midfielder this summer.
“Roma are willing to listen to offers for Radja Nainggolan”
Nainggolan spoke out about his future at Roma last week.
The 29-year-old said: "When you play football you have to make choices and last season my choice was to stay [at Roma].
"We'll see [what will happen this summer]. I'm gong to go on vacation and then we will talk about it."
When pressed on United's interest, Nainggolan added: "It can be true, it can be not true, that's something that you have to know."
Nainggolan is currently under contract in Italy until June 2020.