Although the France international, 26, is not officially suspended, he will "not be available" for selection during the investigation, Liverpool said.
BBC Radio 5 live senior football reporter Ian Dennis said Sakho failed a test after the Europa League victory over Manchester United on 17 March.
It is thought Sakho tested positive for a type of fat burner, said Dennis.
The player has until Tuesday to respond with a B sample.
Sakho, an £18m signing from Paris St-Germain in 2013, has played 34 games this season, including 10 in the Europa League.
He scored in Liverpool`s 4-3 victory over Borussia Dortmund on 14 April which secured their place in the semi-finals.
Liverpool, who are seventh in the Premier League, host Newcastle at Anfield on Saturday.
Sakho`s Liverpool team-mate Kolo Toure was banned for six months in 2011 while at Manchester City after testing positive for a weight-loss drug contained within "water tablets" recommended to him by his wife.
A similar ban for Sakho would rule him out of Euro 2016 in France, which starts on 10 June.
Mamadou Sakho: Liverpool defender investigated over failed drugs test
23 April 2016
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Liverpool defender Mamadou Sakho is being investigated by Uefa after failing a drugs test, AzVision.az reports citing BBC.UK
