Wenger has shown an ability to inspire players - and perhaps most importantly marry the contrasting styles of English and foreign players at Highbury.
Sven Goran Eriksson
Sven Goran Eriksson has won a reputation as one of the most progressive coaches in world football.
The current Lazio boss is highly regarded for his tactical acumen and attention to detail.
He has long been linked with posts in Britain making his name as coach of IFK Gothenburg, Benfica and Sampdoria before moving to Lazio.
He signed a contract to take over at Blackburn in 1997 before reneging; has expressed an interest in the Manchester United job when Sir Alex Ferguson retires; and indicated his desire to become Celtic coach this summer.
A Serie A title with Lazio changed his mind, adding to a list of honours including the Super Cup and European Cup Winners' Cup (with Lazio), Uefa Cup (IFK Gothenburg), three Portuguese titles (Benfica) and the Swedish title (Gothenburg).
With that record of success and his tactical nous, the multilingual Swede would be regarded by many as an ideal candidate to take England. and the English game, forward.
Arsene Wenger
Arsenal manager Wenger is widely regarded as the FA's top choice to succeed Keegan - but it would be a major coup on their part if they could tempt him away from Highbury.
It would also be a major shock to Arsenal, who are so confident Wenger would reject England's offer that they have already agreed to let the FA speak to him, should they so wish.
Wenger has been linked with international football before, mainly in connection with Japan where he has worked successfully.
He will appeal to the FA because of his urbane image and worldwide knowledge of the game. Crucially, Gunners' vice chairman David Dein is also on the FA committee.
Wenger has shown an ability to inspire players - and perhaps most importantly marry the contrasting styles of English and foreign players at Highbury.
He is a huge fan of the bulldog spirit of men like Tony Adams and Martin Keown, while also an advocate of flair.
Wenger is regarded as a progressive thinker, and has also proved a formidable adversary in the psychological games against men like Sir Alex Ferguson.
If the FA pursue Wenger, they would need all their powers of persuasion to convince him to leave behind the day-to-day involvement of Arsenal for the unique challenge of international football.
Roy Hodgson
The former Blackburn manager has been suggested as a candidate because of his knowledge and experience of international football, having taken charge of the Swiss national side.
Hodgson, who has also managed Italian giants Inter Milan, has an excellent reputation on the continent, although is best remembered for spending £7.5m on misfit Kevin Davies while at Ewood Park.
He made his name with Malmo, whom he led to five successive Swedish titles.
He is currently at FC Copenhagen, but is believed to be keen on the job.
Would be an easy target for the national media given the fact that the season he left Rovers, the Lancashire side were relegated.
However, his reputation in the game is undimmed. He is revered in Switzerland for his success with the national team, leading them to the 1994 World Cup and Euro 96.
With Inter, he won the Italian Cup, finished third in Serie A and reached the Uefa Cup final in the one season.
Another highly-respected tactician, he serves on Uefa's Technical Committee.
Terry Venables
Terry Venables has perfected the image of "The People's Champion" after his first spell in charge.
He almost guided England to the Euro 96 final, but his reputation has since been tainted by unsuccessful spells with the Australian national team, Portsmouth and Crystal Palace.
Venables also still has enemies within the FA, still aware of the non-footballing baggage he brought to Lancaster Gate in his short period in charge. Crozier did not rule him out or in at the press conference to appoint Taylor and McLaren.
He will enjoy the support of many fans, as well as influential sections of the media who enjoy his cheery cockney bonhomie.
Venables is tactically astute, and hugely admired and respected by those who played for him.
It would take a major change inside the FA to win him the job back - but the wind of change is blowing through the old place.