Britain's National Crime Agency confirmed on Sunday it was examining the allegations after receiving information from The Sun On Sunday.
The newspaper said an undercover reporter met one player who claimed another agreed to deliberately earn a booking in a recent match in the second-tier of English football in return for a 30,000-pound payout.
"An active NCA investigation is now underway and we are working closely with the Football Association and the Gambling Commission," the NCA said in a statement. "Six people are in custody and are being questioned by NCA officers. We cannot comment further at this stage."
According to the newspaper, the footballer, identified as former Portsmouth and Nigeria defender Sam Sodje, also claimed he could fix Premier League games and added he was capable of rigging matches at next year's World Cup.
Sodje, who presents himself as a fixer, also told the reporter that he was once sent off on purpose for a fee of £70,000.
"We treat any allegations of criminal activity in our competitions with the utmost seriousness," Football League chief executive Shaun Harvey said. "Given that there is an ongoing police investigation into this matter, we cannot comment further at this time. Although, we would encourage anyone with any evidence to report it to the police. We will be giving our full assistance to the police during their investigation."
Portsmouth, now playing in the fourth-tier League two, said it was saddened by the news but distanced itself from Sodje.
"If these serious allegations are true then we are extremely shocked and saddened by them, as match-fixing of any type goes to the heart of the integrity of the game," club spokesman Colin Farmery said. "The player in question no longer plays for the club and we have not been contacted by the authorities, but of course we would co-operate fully with any inquiry."
The Sun On Sunday also reported that Oldham Athletic player Cristian Montano tried to get booked in exchange for a payment in a League One match in October. Oldham immediately suspended the player and announced the opening of an "internal investigation to establish all the relevant facts of the case."
The FA and the Gambling Commission confirmed they are working with the NCA and other authorities on the investigation.
Last month, police made several arrests as part of an investigation into a suspected international betting syndicate that allegedly fixed English football matches. Two players from the sixth tier of English football were charged this week with conspiring to fix matches. Michael Boateng and Hakeem Adelakun, who both play for Conference South team Whitehawk FC, were charged with conspiracy to defraud and are set to appear at Birmingham Magistrates Court on Wednesday.
They were the third and fourth men to be charged in the wake of an undercover operation by Britain's Daily Telegraph, with Chann Sankaran and Krishna Sanjey Ganeshan also scheduled to appear at Birmingham Crown Court.