Agent Gianfranco Cicchetti claims the 20-year-old Argentine star is set for a move to Italy.
"Roma are the frontrunners to sign Manuel Lanzini," Cicchetti told Radio Cooperativa.
"There is an agreement with River to buy him for €10million. In the next few weeks it will be decided whether the deal can be done.
"Lanzini is a crack player and Roma are very interested in completing the transfer.
"The director Walter Sabatini wants Lanzini at Roma because River have a good reputation since they transferred Erik Lamela to the club.
"In addition, there is also the chance of buying a central defender and there are two candidates.
"One of them is Leandro Gonzalez Pirez, also from River, and other one is Lisandro Magallan from Boca. Each of them has a market value of €4million."