The midfielder impressed as Ivo Pulga's side finished a respectable 11th in Serie A last season and has attracted interest from a host of Italy's biggest clubs.
Inter, Roma and Napoli have all been linked with the 25-year-old despite Nerazzurri president Massimo Moratti's insistence they were yet to make an approach, but his current club won't let him go on the cheap.
"We have received a bid for Nainggolan, but we did not deem it to be good enough," sporting director Nicola Salerno told Radio Sportiva.
"I can confirm that Inter and Roma are interested, but we will only accept an offer which will be impossible to refuse."
Nainggolan's agent confirmed the Belgium international had plenty of opportunities to leave the club and hinted that a move away from Serie A could be on the cards.
"We have a number of options to leave Cagliari, but it all depends on (club president) Massimo Cellino," Alessandro Beltrami told Russian newspaper Izvestia.
"Up until now he has never wanted to sell him because he is considered as a key player.
"We’ll just have to wait and see even if the player is ready to consider the idea of transferring to another championship."