The 29-year-old is receiving treatment at the Sports Science Institute in Cape Town, a venue selected by the club’s medical department to aid the England international’s return to fitness.
Lallana has made just three starts and 10 substitute appearances in an injury-ravaged season which did not start until late November because of a thigh injury.
There have been a couple of recurrences of that problem while his latest comeback was ended prematurely on March 31 when he was on the pitch for just five minutes before a hamstring injury forced him off.
Liverpool have taken their time with Lallana in the second half of the season after manager Jurgen Klopp admitted they had probably brought him back too soon from his initial setback.
The club will continue that cautious approach in the final month of the campaign and while the midfielder has not yet been ruled out of their remaining matches he will hope to be able to prove his fitness in time for World Cup consideration.
Meanwhile Liverpool will face Premier League champions Manchester City in the United States this summer.
Liverpool will also take on their arch-rivals Manchester United during the International Champions Cup tournament in July, an event that also features Arsenal, Chelsea, and Tottenham.
The six Premier League sides will be joined by the likes of Barcelona, Real Madrid, Bayern Munich, Juventus, AC Milan and Paris St Germain in the competition.
Each of the Premier League sides will play three fixtures, which will form part of their pre-season preparations.
City will meet Borussia Dortmund in Chicago on July 20 before facing Liverpool, who ended their Champions League challenge earlier this month, five days later in New Jersey. They also play Bayern in Miami on July 28.
Liverpool also play Dortmund, in Charlotte on July 22, before taking on United at the 107,000-capacity Michigan Stadium on July 28.
United’s other games are against Milan at the Rose Bowl in Los Angeles on July 25 and Real Madrid in Miami on July 31.
United have also arranged friendlies against Club America and San Jose Earthquakes during their pre-season tour.