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.
But Calciomercato say the Serie A side are willing to listen to offers for Nainggolan, with Chelsea and Manchester United keen.
They reckon the EPL 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.
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.”
Support InfoStride News' Credible Journalism: Only credible journalism can guarantee a fair, accountable and transparent society, including democracy and government. It involves a lot of efforts and money. We need your support. Click here to Donate