The Enquirer understands that the investigation involves allegations of corruption during the award of contracts and centres on the Thameslink Farringdon Station project.
The arrests are believed to include the head of a leading construction company which supplied labour on the project.
British Transport Police confirmed that four people were arrested and have now been bailed.
Police are understood to have raided the offices of the construction company involved last month and seized documents and computers.
Police are not naming the firm involved but its identity is widely known in the London market.
A Network Rail spokesman confirmed that no Network Rail employees have been arrested as part of the investigation.
A Laing O’Rourke/Costain joint venture is main contractor at Farringdon.