Black had denied making any suggestion, to undercover reporters from The Daily Telegraph posing as representatives of a Far Eastern firm, about payments to club officials during transfer negotiations.
"Despite numerous requests to provide the club with any evidence relating to the allegation against Mr Black, none has been forthcoming," the Premier League club said in a statement on Thursday.
"There is no evidence of any wrongdoing, and as such, the club now considers the matter closed. Eric Black retains the full support of Southampton Football Club."
Allardyce lost the job of England manager on Sept. 27 after 67 days in charge.
The FA found 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 also sacked assistant head coach Tommy Wright after allegations in the same paper that he accepted a cash "bung" of 5,000 pounds ($6,484). Wright denied any wrongdoing.
(Reporting by Alan Baldwin, editing by Toby Davis)
