The Serie A giants reportedly have an agreement in place to sign the 23-year-old striker from Chelsea this summer on an initial loan deal with a mandatory purchase clause.
Roma are keen on signing him on an initial two-year loan with the purchase clause set at €35m.
Abraham is yet to be convinced about a move to Roma and is keener on joining Arsenal, who are also interested in the striker.
According to Italian daily Il Messaggero, Roma are now ready to halve the length of the proposed loan deal in order to show how serious they are about Abraham.
It has been claimed that the Serie A giants are now prepared to sign him on a one-year loan with the purchase clause potentially activated next summer.
Jose Mourinho has also called Abraham personally to convince him to join the Giallorossi.
There are claims that Roma general manager Tiago Pinto will soon be in England to attempt to complete the signing of Abraham this week.
Chelsea would prefer to sell him to Roma over the prospect of seeing the striker join Arsenal.
