The midfielder has just come off an impressive Club World Cup campaign with Palmeiras and is expected to leave for Europe this summer.
Inter and Porto are in contact with Palmeiras for Rios, but Roma are now moving to outbid all rivals.
Il Corriere dello Sport says Roma are offering €20m up front plus €5m in bonuses to Palmeiras and are confident the deal is "under control".
Rios also has a contract offer in front of him from Roma worth €2.5m-a-year.
Related：
Palmeiras
Roma
Internazionale
Porto