West Ham director Mike Lee has revealed that Gianfranco Zola and Roberto Donadoni "really shone" in interviews for the vacant managerial position.
Zola was interviewed by club officials for a second time in Rome on Sunday.
BBC Sport understands Croatia coach Slaven Bilic is virtually out of the running because he wants to combine the job with managing his country.
Former Getafe coach Michael Laudrup is also out of the running after the Dane agreed to take the Spartak Moscow job.
"Ideally we would like to have a manager in place for the West Brom match next week"
But Lee suggested West Ham might still try to talk to him to assess the possibility of Bilic returning to Upton Park.
Lee added: "That is a discussion that would have to take place with the Croatian FA and with Slaven himself, but is it unlikely that it will be possible until after the England game.
"Ideally we would like to have a manager in place in time for the West Brom match next Saturday, or if not in the stands, and in place for the Newcastle game the following week."
Alan Curbishley resigned as manager on Wednesday, unhappy at the club's transfer policy, and the Hammers have wasted little time seeking a new man.
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"John Collins is very strong and will be an excellent manager in due course. He truly impressed but is maybe not quite right at the moment," Lee told Radio 5 Live's Sportsweek.
Zola is joint coach of the Italian Under-21 side and assisted another ex-Stamford Bridge player, Pierluigi Casiraghi, with their national squad at the Olympic Games.
Donadoni guided Italy to the Euro 2008 quarter-finals but lost his job after the tournament as the Italian Football Federation re-appointed Marcello Lippi.
Donadoni, who has coached Serie A sides Livorno and Genoa, speaks English after spending two seasons playing in Major League Soccer in the United States.
Former Denmark striker Laudrup, 44, has been linked with several jobs in Europe since he resigned as coach of Spanish club Getafe.
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