Uvini had six months at Tottenham last season.
"Following Bruno are about four or five teams," Emanuele Ricci told Il Romanista.
"The transfer market has just begun and I do not exclude that in the coming days there will be important developments.
"Roma, for some time, have been following the boy, but it is another step to buying him. They are interested, but so are many teams, so there is nothing concrete.
"His price is around 3m and he wants to move to Italy."