France's RMC radio reported that Sakho had failed a dope test following the use of a fat-burning drug as an aid to weight loss.
Liverpool, playing relegation-threatened Newcastle United in the Premier League at Anfield later on Saturday, did not provide details of the substance but said they had received a formal communication from UEFA on Friday.
A club statement said that UEFA was "investigating a possible anti-doping rule violation by Mamadou Sakho" and the player would respond to European soccer's ruling body.
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"The player is currently not subject to any playing suspension," Liverpool added.
"However, the club, in consultation with the player, has decided that while this process is followed the player will not be available for selection for matches."
Liverpool are seventh in the Premier League, with four games remaining, but could qualify for the lucrative Champions League next season if they win the Europa League.
The former European champions have reached the semi-finals of that second tier European competition after beating Borussia Dortmund 5-4 on aggregate in a stirring quarter-finals fightback last week.
They are due to play Villarreal of Spain in the semi-final first leg on April 28 with the return at Anfield on May 5.
Sakho grabbed the equaliser at 3-3 against Dortmund in the quarter-final second leg, which Liverpool won 4-3 in stoppage time, and scored against Everton in a 4-0 rout in the league on Wednesday.
The Liverpool Echo reported that Sakho, 26, had tested positive after the Europa League round of 16 game against Manchester United on March 17.
Sakho's Liverpool team mate Kolo Toure was banned for six months in 2011 while at Manchester City for a similar failed drugs test.
A similar ban for Sakho would rule him out the European championship being held in France.
(Reporting by Alan Baldwin, editing by Ed Osmond)
