The south coast club have been notified by the paper that they will be releasing an article on 52-year-old Black on Friday but did not disclose the accompanying information.
A statement on southamptonfc.com read: "Southampton Football Club has today been made aware by The Daily Telegraph that, as part of their on-going investigation, the club's Assistant First Team Manager Eric Black will feature as part of an article in tomorrow's paper.
"The club immediately requested to be sent, by The Daily Telegraph, the details of this article, but the newspaper declined to share any further information.
"We have today contacted The FA and The Premier League, and intend to work closely with both bodies on this matter when the facts become clear.
"Southampton Football Club is fully committed to investigating any situation that directly or indirectly relates to our club, employees or the wider community."
Former Aberdeen star and Scotland international Black joined Southampton in the summer following stints with Aston Villa, Rotherham United, Blackburn Rovers, Sunderland and Birmingham City, acting as caretaker manager with all clubs.