Jack Shepherd's lawyer has said that the speedboat killer is unlikely to fight extradition and could return to the UK this week.
Shepherd is currently imprisoned in Tbilisi, Georgia, after handing himself in to the authorities in February.
The 31-year-old went on the run while facing trial over the death of Charlotte Brown, 24.
His speedboat overturned on the River Thames while the pair were on a Champagne-fuelled first date in December 2015.
He was convicted of manslaughter at the Old Bailey and sentenced to six years in jail after Ms Brown, from Clacton-on-Sea, Essex, died after plunging into the icy water.
Shepherd's lawyer Tariel Kakabadze said there is a "very big chance" Shepherd will not fight extradition to the UK and wants to participate as he challenges his conviction in the Court of Appeal.
The next hearing in Georgia could be set by the judge on Monday, he said, adding: "If he agrees with the extradition request, he might return to the UK this week."
Web designer Shepherd, originally from Exeter, may seek certain "reassurances" before agreeing to the request, which was sent to the Georgian authorities by the Home Office, the lawyer suggested.
