There are reports Alexander Doni has rejected an offer from Liverpool, while Julio Sergio's agent denies talks with Genoa and Siena.
Roma have confirmed they will bring in a top new goalkeeper over the summer, so must place some of their current players.
Last week the Giallorossi confirmed they had agreed a fee with Liverpool for Brazilian Doni, so he has been in talks over personal terms.
However, according to Sky Sport Italia, the 31-year-old has turned down the €900,000 per season contract, as he currently earns €2.5m at Roma.
He is also of interest to Galatasaray should they fail to secure a deal for Lazio goalkeeper Fernando Muslera.
Another of Roma's shot-stoppers, Julio Sergio, has been heavily linked with Serie A sides Genoa and Siena.
“We have not received any proposals from Genoa or Siena,” said agent Alessandro Lucci.
“We are discussing the situation and trying to find the best solution for Julio, as he is eager to play first team football. He has interest from Italy and overseas.”