Nainggolan has been at Roma since 2014 and grown into one of their most important players.
But the departure of manager Luciano Spalletti has thrown the futures of several players into doubt.
Liverpool are keen on signing Mohamed Salah, Antonio Rudiger has been linked with the Premier League and now Nainggolan has refused to deny the rumours surrounding him.
When asked by Sky Sports what he thought about the links with Manchester United, the 29-year-old midfielder told Sky Sports: "It may be true. It may not be true.
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It may be true. It may not be true
"We'll see. I am going on holiday and then we will talk about it.
"My thoughts are to go on holiday and relax myself, I am not thinking about my future right now.
"I've spoken enough about this and what I want. I have made a promise [to Roma] that I intend to maintain; now it's up to other people."
Nainggolan was heavily linked with Chelsea last summer but when they were unable to agree a deal, the Blues moved on to N'Golo Kante.
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Radja Nainggolan was coy about rumours linking him with Manchester United
United are also interested in Nainggolan's international team-mate Romelu Lukaku.
And the Everton striker revealed yesterday he had agreed a deal with another club, saying: “For the time being, England is the best for me.
“My business attorney is now talking to a club. I know where I want to go. I just stay patient. I know that appointments have been made. I’m just waiting for a call.
“I’m now six years in the Premier League, I know the competition inside out. I’m almost 100 goals in the league, which is a milestone I want to achieve.
“The Premier League is a dream for me. I want to win the Premier League as often as possible. But I also want the Champions League, the FA Cup and all the other prizes.”