That's according to the Daily Express, who report that the Belgian international has caught the eye of Mourinho, Van Gaal and Wenger - with the three Premier League managers considering a bid to bring him to England.
Nainggolan only joined Roma permanently last summer - the club in the Italian capital paid Cagliari £7m for 50 per cent of his playing rights.
Cagliari still own half of his rights, and they want £13m to sell their 50 per cent of Nainggolan. The report claims Roma would be happy with £13m for their half, meaning that a Premier League club would have to shell out £26m to sign him.
The 26-year-old is reportedly open to a move to the Premier League one day, but is keen to stay in Italy for the time being after settling well in Rome.
He joined Roma on loan last year, making 17 Serie A appearances and scoring two goals. They were clearly impressed, and he's gone from strength to strength under Rudi Garcia in Rome.
Southampton were linked with the player when he was still at Cagliari, but now the Champions League big boys are circling.
Belgium's incredible surplus of talent in central midfield means that Nainggolan has only made eight national team appearances, but he's a player of real quality.
Arsenal are looking for a new combative box-to-box central midfielder, and Nainggolan would fit the bill perfectly. A centre-back is a priority this month though, so any move would likely not be forthcoming until the summer at the earliest.
The same goes for Manchester United, who have a transfer priority at centre-back as well.
As for Chelsea, reports today claim they're closing in on Juan Cuadrado, the Colombian winger currently at Fiorentina in Italy.