Lallana had previously been speeding along his recovery at Liverpool's Melwood training base but they have decided to send him to the Middle East as he nears his return to first-team football.
The England midfielder is yet to play a single minute of competitive football for club or country this season, after suffering ain injury in a pre-season friendly against Atletico Madrid.
Speaking last month about his recovery, the 29-year-old said: "I'm getting on well - slowly but surely in the background. It's going as well as it can. I'm obviously looking forward to getting back."
Liverpool boss Jurgen Klopp said at the time of the injury that Lallana would be out for "a couple of months" but gave no exact timescale for the player's return.
Gareth Southgate recently bemoaned Lallana's absence and described his as an important "link player" for England.
He said: "In my year in charge, Adam Lallana has been our best player and we've not had him for the last three matches."
The clinic which the Reds midfielder has travelled to describes itself as the "world's leading specialised orthopaedic and sports medicine hospital, staffed by some of the world's leading medicine practitioners and researchers."
They have previously treated top players including John Obi Mikel, Eidur Gudjohnsen and Jack Butland.