Sky Sports sources understand Roma goalkeeper Alexander Doni will undergo a medical at Liverpool on Tuesday.
The 31-year-old's agent said last week that a deal was imminent following several weeks of negotiations.
An initial move broke down earlier in the summer after Doni failed to agree personal terms with Liverpool.
But the Brazilian could complete his move to Anfield this week after an agreement was reached with Roma.
Doni would only provide back-up to Kenny Dalglish's first choice, Jose Reina, but would offer an experienced deputy.
Liverpool on Sunday departed for a pre-season tour of the Far East, but members of the medical staff will still be available to oversee Doni's medical.