Kovacevic has received widespread publicity in England for using a controversial treatment involving the use of fluids derived from horse placenta to speed up the healing process.
Related ArticlesChelsea v Wolves: match previewSergio Ag?: the best bitsNapoli deny Marek Hamsik move to ChelseaKalou dropped over training ground fightChelsea close in on £40m Ag?Ashley Cole backs Chelsea chase for Ag?Liverpool's Albert Riera, Yossi Benayoun, Fabio Aurelio and Glen Johnson have also travelled to Serbia for 'special treatment' according to the club's website as has Arsenal's injured forward Robin van Persie.
Lampard sufferd his injury on Nov 12 and Premier League leaders Chelsea said he would likely be missing for three weeks ruling him out of a London derby at Arsenal on Nov 29.
Liverpool said midfielders Riera and Benayoun were due to be out for another two weeks with hamstring problems but could now feature against Manchester City at Anfield in Saturday's early kickoff after the much-publicised journey to eastern Europe.
Benitez was so pleased with the treatment he sent defenders Aurelio and Johnson to Serbia as well.
All four players have since returned to Merseyside and have taken part in full training sessions for the past two days.
"You know people have talked about them going to Serbia for special treatment and that's true," Benitez said. "We had a lot of reports of international players going there, so we sent some players.
"They are now training so we will see if they can play. They have trained for the last two days. It has been good.
"There are other names from different teams who have been doing this treatment for seven years. It is a curative programme for players with muscle injuries and it works well."
Arsenal's Van Persie has visited Kovacevic for treatment on the ankle ligaments he damaged playing for the Netherlands last Saturday, which the club said would keep him out for six weeks.
Arsenal said that Van Persie's quest for a speedy return led him to Serbia where one procedure will see placenta fluid dripped onto his ankle.
Arsenal manager Arsene Wenger told reporters at a news conference that while he was happy to let Van Persie experiment, he was sceptical of the impact of alternative medicine.
"When you have, for example, a muscle problem, it's 21 days (out)," he said. "I've never seen anybody shorter.
"I have seen so many people sent there (Serbia) and in five days they can play. But they can only play with injections and then they have a recurrence of a muscle injury always.
"You cannot shorten it (the recovery period). The intensity of the treatment can help and sometimes you can speed it up a little but there are some problems. A damaged ankle ligament takes four weeks."
However, the Arsenal manager added that he did not object to placenta treatment on ethical grounds.
"It's not injected," he said. "I leave that responsibility to my medical people. I ask is there any danger to do it, they say no, I say OK let's let him go and that's it."