The USA captain has been undergoing medical evaluations since last month, his club Seattle Sounders revealed.
The 33-year-old, who spent seven years playing in England, returned to training with Seattle on Wednesday.
"You can't just say, 'Clint's important to us'. You have to mean it. And that means Clint's health comes first," said Seattle general manager Garth Lagerwey.
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But the Belgian capital remains on the highest alert level, with hundreds of armed police and soldiers on patrol.
Authorities fear Paris-style attacks may be carried out, as at least one Paris gunman had lived in Brussels.
France says 130 people died in a series of attacks in Paris. At least one suspected attacker is still at large.
The so-called Islamic State (IS) group says it carried out the attacks.
Five people have been charged in Belgium with terrorism offences in connection with the attacks in the neighbouring country.
In Brussels, public transport was due to start running again from 06:00 (GMT) though some metro lines will remain closed.
Abdelhamid Abaaoud, the suspected ringleader who was killed in police raids in the Parisian suburb of Saint Denis, was near the Bataclan theatre during a deadly siege there, it has emerged.
French officials say mobile phone data also show he returned to cafes and restaurants targeted in the attacks. They say there is evidence that Abaaoud was planning an attack on the La Defense business district.
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On Tuesday, an arrest warrant was issued in Belgium for a man named Mohamed Abrini over the attacks.
Prosecutors say that two days before the attacks, he was seen driving a car with suspect Salah Abdeslam at a petrol station on the motorway to Paris.
Abrini is described as "dangerous and probably armed".
Abdeslam is currently the subject of an international manhunt after the attacks.
The Renault Clio that Abrini was seen driving was later used in the attacks, prosecutors say. Police say he should not be approached by the public.
Belgian prosecutors also said on Tuesday that they had partially identified two other men taken into custody.
The men, named as Ali O and Lazez A, are both from the Brussels district of Molenbeek, and both will appear separately in court during the course of this week.
Also on Tuesday, French President Francois Hollande met US President Barack Obama in Washington where the two leaders re-iterated their commitment to eradicating IS.
Mr Obama said there would be increased co-operation with France to hit IS targets in Iraq and Syria, and called on the EU to finally implement an agreement that would require airlines to the share passenger information.

Private Derby XXX was promoted to the rank of lance corporal at an event in Chester marking eight years of the Mercian Regiment.
He was awarded his honour by the colonel of the regiment, Brigadier Andrew Williams.
The Swaledale ram, who is officially classed as a soldier, received his promotion for "good behaviour".
He is the 30th in a line of mascot rams running back to the Indian Mutiny War in the mid-19th Century.
The first Private Derby was acquired in 1858 by the 95th (Derbyshire) Regiment of Foot and became the mascot of the Mercian Regiment when it formed in 2007.
Lance Corporal Derby XXX joined the regiment in February 2014.
He has his own army number, gets paid to buy his rations and takes his holidays during the mating season on the Chatsworth Estate in Derbyshire.
During his career, Lance Corporal Derby XXX has also helped switch on the Christmas lights in Ashbourne and met Prince William at the unveiling of a memorial commemorating the 1914 Christmas Truce.
Former Tottenham and Fulham forward Clint Dempsey has undergone a procedure to address an irregular heartbeat.
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The Brussels metro and schools are due to reopen after they were shut four days ago in a security crackdown following the Paris attacks.
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A sheep which is the mascot of a British Army regiment has been promoted at a ceremony marking its formation.