The Daily Telegraph reported on Thursday that Black, 52, met a bogus representative of a Far East firm on Sept. 2 at a hotel in Hampshire who said he was interested in English football's billion-pound transfer market.
Black told the newspaper on Thursday that he denied making any suggestion to their undercover reporters that football officials should be paid during transfer negotiations.
After being made aware that Black would feature in the Telegraph article, the club issued a statement on their website (southamptonfc.com) saying: "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."
Black, who was on the Southampton bench for their Europa League group game against Hapoel Beer-Sheva in Israel on Thursday, joined the south-coast club as an assistant to their new French manager Claude Puel on June 30.
Allardyce lost the England job on Tuesday after the FA said he had behaved inappropriately following secret filming that showed him offering advice to businessmen on how to "get around" rules on player transfers.
English second-tier club Barnsley sacked assistant head coach Tommy Wright on Thursday after allegations in the Telegraph that he accepted a cash "bung" of 5,000 pounds ($6,484.00). Wright denied any wrongdoing.
The Telegraph said its secret filming showed Wright accepting the bung after agreeing to help a fake Far Eastern firm which wanted to profit from transfers.
($1 = 0.7711 pounds)
(Writing by Ken Ferris; Editing by Mitch Phillips)
