An announcement on the successor to Sir Dave Richards, who has been chairman since 1999, is due before the end of the season and could be made as early as this week.
Press Association Sport understands Hoffman, a former vice-chairman of Coventry, is being spoken about in club circles as the man most likely to get the position.
He has developed close links with the Premier League ever since he signed a groundbreaking sponsorship deal in 2001 when he was chief executive of Barclaycard.
Hoffman went on to become vice-chairman of Barclays - which is still the Premier League's lead sponsor - and then rescued the stricken Northern Rock after taking over as chief executive during the credit crunch.
In 2011, he was appointed to the unpaid role of chairman of the Football Foundation, Britain's largest sports charity that awards millions of pounds in funding to grassroots projects every year.
Another candidate for the Premier League position is Sir Keith Mills, the vice-chairman of the London 2012 Olympics and a director of Tottenham.
It is understood that Mills has held talks with headhunters about the chairmanship.
- Sports & Recreation
- Sir Dave Richards