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."