The main allegations don't center on players affecting the results of a game, but rather on things like deliberately earning yellow cards. Many bookmakers allow people to bet on whether a certain player will be booked.
The Sun reported that officers were likely to look at a yellow card Campbell received for a tackle committed in the first half of Blackburn's game against Ipswich on Tuesday.
According to the newspaper, former Portsmouth and Nigeria defender Sam Sodje claimed he could fix Premier League games and was capable of rigging matches at next year's World Cup.
Sodje, who played in the Premier League for Reading, also allegedly told an undercover reporter that a player deliberately sought to get booked in a recent League Championship match in return for a 30,000-pound payout.
Sodje, who presented himself as a fixer, also told the reporter that he was once sent off on purpose for a fee of 70,000 pounds.
The allegations alarmed his former club, with Portsmouth announcing it would be summoning its players to a meeting on Tuesday to warn them about the threat posed by fixers.
"All you can do is check the people around you, notice anything suspicious and inform the players how serious an issue this is," Portsmouth chief executive Mark Catlin said. "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."
At least one League One player is also under investigation, with Oldham confirming Cristian Montano had been arrested and suspended by the club.
Montano tried to get booked in exchange for a payment in a League One match in October, according to The Sun.
"Anybody who saw that Sky News report will have been devastated and sick to their stomachs," Oldham manager Lee Johnson said on the club's website, referring to television coverage. "However, we have to let the authorities do their job and duties, and we cannot prejudice that."
Britain's National Crime Agency has not identified any of the people arrested, but said Monday that five were released on bail the previous evening until April, while a sixth was still being questioned.
"The NCA can confirm that the Sun on Sunday has passed material from its own investigation to the National Crime Agency," the London-based agency said in a statement. "An active NCA investigation is now underway and we are working closely with the Football Association and the Gambling Commission."
The NCA is also investigating an alleged international illegal betting syndicate following an undercover investigation by the Daily Telegraph which led to two players from the sixth tier being charged with conspiring to fix matches last week.
- AP