Rios is wanted by clubs across Europe, but Roma have emerged as favourites to clinch his signing.
La Gazzetta dello Sport says Roma are offering €28m plus €3m in bonuses for Rios.
The midfielder has already expressed his willingness to work under new Roma coach Gian Piero Gasperini, accepting a five-year contract and giving up the 10% of his contract rights that he would be entitled to.
All this is driven by his desire to compete in a competitive tournament like our Serie A.