Despite reports to the contrary elsewhere, Andy Flower, Martyn Moxon and Tom Moody have all informed ESPNcricinfo they are not pursuing an interest in the role. Clare Connor ruled herself out in the early stages, while Wasim Khan has instead accepted an offer to move to Lahore as MD of the Pakistan Cricket Board.
That leaves a field that includes Giles, currently director of sport at Warwickshire; Mick Newell, the Nottinghamshire director of cricket; Mark Nicholas, the writer, broadcaster and former captain of Hampshire, and Ronnie Irani, the former England all-rounder.
While Giles and Irani are understood to have been offered interviews by the ECB - one has taken place; the other is next week - Nicholas is understood to be mulling over an approach from a headhunter and has yet to fully commit to the process. Candidates have been required to put together a presentation to the ECB before the interview.
Strauss decided to step down after his wife was diagnosed with cancer. Flower has filled the role in an interim capacity.
If Giles is appointed it would complete a remarkable comeback. He was sacked by Paul Downton, the England team director at the time, as England's limited-overs coach at the start of 2014 - barely six months after leading England to the brink of their first global ODI trophy - but has subsequently lead Lancashire and Warwickshire to trophies (The T20 Blast at Lancashire in 2015 and the Division Two title at Warwickshire in 2018) and served on several ECB working parties. He has also worked as an England selector, is an Ashes winner and led Warwickshire to the Championship title as coach in 2012.
Irani offers strong competition, though. As chairman of Essex's cricket committee, he was in a large part responsible for the club embracing a home-grown policy that helped them win the Championship in 2017 and helped the club sustain their excellent reputation for developing players. He also has a business background which will be deemed important for an ECB that is keen to cut costs across the board and at Loughborough in particular.
The ECB hope to have someone in place before England head to the Caribbean in January, though an announcement next week is more than possible.