The two clubs reached an agreement last month for Doni to join the Reds on a free transfer, with the 31-year-old expected to sign a two-year contract.
"Everything is okay with Liverpool," Doni's agent Ovidio Colucci told asromanews.it. "We are returning to Rome to sign the final documents."
He added: "The deal will be finally completed tomorrow (Friday) and Doni will be back at Liverpool on Sunday to be available for [Liverpool manager Kenny] Dalglish."
Doni moved to Roma in 2005 from Juventude and is under contract at the Serie A outfit until 2013.
He has been understudy to Julio Sergio in recent seasons, but made 16 league appearances for Roma last term.
Source: PA