Six people have been detained in an investigation by the National Crime Agency after it acted on information passed to it by the Sun on Sunday newspaper.
According to the paper, an undercover investigator met former Portsmouth player Sodje, who allegedly said he could arrange for footballers in the Championship to get themselves a yellow card in return for tens of thousands of pounds.
The 34-year-old, who played for Portsmouth in League One last season, claimed he could rig Premier League games and even said he was preparing to fix matches at next year's World Cup in Brazil, the newspaper reported.
Fratton Park chiefs will speak to their current players about the claims and warn them to be vigilant.
Chief executive Mark Catlin said: "All you can do is check the people around you, notice anything suspicious and inform the players how serious an issue this is.
"We will be doing that tomorrow as a club, speaking to the players and saying we have to be self-policing.
"If anyone sees or hears anything suspicious it's not a case of dropping a friend in it, it's about upholding the integrity of the sport.
"Things like this need to be dealt with internally. The people who will root this out are the players, the managers and the people within football."
The claims overshadowed Pompey's appointment of new manager Richie Barker and director of football Steve Coppell.
The club were naturally unwilling to discuss the allegations as Barker was presented to the media on Monday morning.
But Pompey chairman Iain McIness did say: "I think the gaming industry shouild be held to account. Somebody can sit on their laptop and check out of a bet, you don't even have to win the bet now. There is just too much of it.
"It's inevitable if you make betting as big a business as it is now available to sport in that depth, you are going to have a bunch of characters that are just going to do things you shouldn't be expected to do."