The programme claimed illegal payments were rife in England's Premier League.
"We've been talking to the Football Association and have already arranged to meet with them on Monday," said a BBC spokesperson.
Bolton manager Sam Allardyce and his son Craig, who were at the centre of the allegations are considering legal action.
"I am very angry at the lies told about me. The individuals who appeared in the programme making accusations against me have already confirmed in writing to my lawyers that they lied to the BBC," he said earlier this week.
"They lied in the hope of being able to make millions offered by the BBC undercover reporter to buy their sports agency businesses.
"As a result of their greed my good name has been tarnished by deceit and innuendo.
"I am determined to clear my name and have asked my lawyers to determine my next steps."
Others implicated in the programme were agents Charles Collymore and Peter Harrison, Portsmouth manager Harry Redknapp and Newcastle assistant manager Kevin Bond.
Harrison is also considering legal action.
"I've never given bungs. I've not given a bung to Sam Allardyce. I've never given a bung. I shall be suing the BBC,” he said.
"I haven't heard from the FA. I shall be carrying on as an agent and I shall be doing whatever the FA want me to do."
A joint probe by the FA and Premier League will also be launched into claims by Harrison that Chelsea's director of youth football Frank Arnesen, Liverpool and Newcastle had all offered a Middlesbrough youth player money to move to their clubs.
Meanwhile, the FA have also confirmed they will contact Blackpool chairman Karl Oyston and leading agent Jon Holmes to ask them to provide further information on their claims they were offered and asked for bungs respectively.
Oyston claims the issue of bungs is still a major problem in football and that he has been offered bribes by agents on a number of occasions.
Holmes, chief executive of SFX Europe, claimed three managers, one of them currently at a Premiership club, had intimated they wanted a kickback.