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The Daily Mail has reported that Berahino was banned after testing positive for a recreational drug following an out-of-competition test in September.
Hughes did not confirm why Berahino was suspended, but said Stoke was aware of the matter prior to signing the highly-rated striker in a £12 million deal.
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"We are aware of it, clearly," Hughes told his weekly press conference. "There was an FA disciplinary matter and Saido had an eight-week suspension, I believe. We were aware of that before we signed him.
"In terms of more detail, you would probably need to refer back to his former club. We aren't in a position to give any more details as we don't have them.
"He had issues at his previous club for 18 months, which this is obviously a part of. As with all players, we did our research on him before we signed him, but that didn't change our thinking at all. We are pleased with what he is producing and he is looking forward to the game tomorrow."
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The Football Association has declined to comment on the matter.
Stoke visit Berahino's former club West Brom on Saturday and Hughes said he had no qualms about playing him.
"Why wouldn't I play him?" the Welshman said. "He is in line to be involved. He came on to good effect on Wednesday and there is no reason why he shouldn't be involved tomorrow."
Berahino, 23, made his Stoke debut as a substitute in Wednesday's 1-1 draw with Everton. It was his first competitive appearance since West Brom's 1-0 loss at Bournemouth on September 10.
The former England Under-21 international burst onto the scene in the 2014-15 season, when he finished as West Brom's top scorer with 20 goals in all competitions.
But he fell out with West Brom manager Tony Pulis and chairman Jeremy Peace after being denied a move to Tottenham Hotspur in August 2015, resulting in a long-running contract dispute.
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