Benayoun and Riera had been expected to be sidelined for up to five weeks after suffering torn hamstrings during Liverpool's 2-2 draw against Birmingham City at Anfield 11 days ago.
Related ArticlesLiverpool sign MoliBenítez: I have failed if Liverpool don't win titleLiverpool could sell quartet to balance booksSteven Gerrard fit to face Man CityBenitez sets record straightSport on televisionBut the midfielders have now been given an outside chance of facing City at Anfield this weekend after making unexpected progress with their injuries after visiting Mariana Kovacevic in Belgrade. Israeli midfielder Benayoun said: 'I am feeling better already. My hope now is that I will be fit in one week, two at the most. '
Kovacevic has sprung to prominence following Arsenal forward Robin van Persie's revelation that he would be visiting her Belgrade clinic in an attempt to boost his recovery from an ankle injury suffered while playing for Holland against Italy at the weekend.
Dutch team-mate Orlando Engelaar had recommended Kovacevic to Van Persie after making a quicker than expected recovery from injury after being subjected to her innovative methods earlier this year.
The injection of horse placenta on to the affected area is claimed to speed up the recovery process and, while it is not known whether Benayoun and Riera have been subjected to that treatment, both have returned to Liverpool ahead of schedule with their rehabilitation.
David Ngog, the French forward, is expected to be fit to face City, despite suffering a broken nose while training with France Under-21s this week.
Ngog, whose last outing for Liverpool ended in controversy amid accusations that he dived to win a penalty against Birmingham, will be able to take his place in the squad for City's visit, according to manager Rafael Benítez.
Benítez said: 'Ngog has broken his nose, so we will have to see how he is before the weekend, but we think he is going to be OK. It is not too serious.'
Liverpool face a crucial week with the visit of City followed by the Champions League trip to Hungary to tackle Debrecen, where even a victory may not be enough to save Benitez's team from elimination.
Benítez said: 'This is the start of an important week for us.'