The seven footballers are aged between 18 and 30, BBC reported citing the National Crime Agency (NCA) as saying. It added that six other men originally arrested in December on suspicion of involvement in match-fixing, then later bailed, have been re-arrested.
"The investigation began following receipt of material from the Sun on Sunday. It remains ongoing and we cannot provide further detail at this stage," the NCA said.
All 13 are currently being interviewed by police over allegations of bribery and money laundering.
"The FA has been made aware of developments in relation to an ongoing NCA investigation, including a number of further arrests. We are liaising with the authorities in relation to these allegations. The FA will make no further comment at this time," the English Football Association said in a statement.
"The Football League has been made aware that a number of arrests have been made in relation to an ongoing police investigation. We will provide our full co-operation to the relevant authorities. Given that it is an ongoing matter, we cannot comment further at this time," a spokesperson for the Football League said.