Lord Stevens is due to publish the initial results of an official inquiry into alleged corruption in football.
Lords Stevens will ask for more time to investigate some transfers
The ex-Metropolitan Police commissioner examined 362 transfers and while most were conducted properly, over 50 are thought to require further scrutiny.
The inquiry began in March after claims of corruption in the game from Luton Town manager Mike Newell and former England coach Sven Goran Eriksson.
There have since been more allegations of illegal payments known as 'bungs'.
Lord Stevens will ask the Premier League club chairmen for more time to investigate transfers that need more scrutiny.
The individuals and clubs involved in them will not be made public.
Many of them are thought to involve players signed from overseas.
More transparency required
Lord Stevens is expected to call for stricter transfer regulations and for more transparency in the way players are bought and sold.
Mr Newell told BBC's One Panorama programme that freelance football agent Charles Collymore offered him a cut of a player's fee that he tried to negotiate.
The Luton Town manager said he rejected the offer and reported the agent to the Football Association.
Mr Collymore denies offering or accepting any bungs, which are illegal payments made during transfer dealings.
He was secretly filmed for the BBC programme, Undercover: Football's Dirty Secrets, and said he knew eight Premiership managers who would accept bungs.