The Liverpool midfielders were flown to Belgrade earlier this week to see Mariana Kovacevic, the physiotherapist who has become famous for curing injured sportsmen with liquid from horse placenta.
Both men were expected to be sidelined for between three to five weeks after they sustained the injuries against Birmingham last Monday.
But their condition has improved so much since seeing Kovacevic there is an outside chance of them being available for Saturday's home clash with Manchester City.
Benayoun has been in outstanding form this season and he is quietly confident he will be back in action sooner rather than later.
'I have been in Belgrade to see her and I am feeling better already,' Benayoun confirmed. 'My hope now is that I will be fit in one week, two at the most. I have a good feeling about it.'
If either of Benayoun or Riera were available after their special treatment it would be another huge boost for Rafa Benitez, who is getting close to having his strongest team available for the first time this season.
Though neither Fernando Torres or Fabio Aurelio will be available, Steven Gerrard, Daniel Agger and Glen Johnson are all expected to figure, while David Ngog should also be included despite breaking his nose with France's Under-21s.
Ngog's last appearance for Liverpool was shrouded in controversy after he 'won' the penalty that enabled his side to secure a 2-2 draw with Birmingham.
That incident, though, overshadowed what had been an encouraging display - he scored the Reds' opener - and with Torres set to be sidelined, Ngog will be needed.
'Ngog has broken his nose, so we will have to see how he is before the weekend,' Benitez said today. 'But we think he is going to be okay. It is not too serious.'