The Villans tabled their initial bid on Tuesday for Reo-Coker, who has made it clear he wants to join a club "where he feels wanted".
But sources close to the Hammers indicated they are in no hurry to accept Villa's opening offer for the former Wimbledon player who cost £500,000 when he moved to Upton Park in January 2004.
Villa manager Martin O'Neill has targeted Reo-Coker as one of his main summer targets as Gavin McCann's days look numbered, while there is a question mark over the future of Steven Davis.
In an ideal world Villa and Reo-Coker would like to tie the deal up in the next 48 hours - with the player forming a midfield partnership with Gareth Barry and Stiliyan Petrov.
The player now has two days off before captaining England Under-21s in the European Championship finals in Holland.
Reo-Coker had been linked strongly with a move to Newcastle in part exchange for Scott Parker, who is heading for Upton Park.
But that deal was scuppered once Joey Barton was lined up to move to St James' Park from Manchester City as a replacement for Parker.
Reo-Coker's agent Tony Finnegan has been making optimistic noises for the past few days about the player joining Villa.
He was the subject of interest from Arsenal during the January transfer window, although nothing was firmed up by the Gunners.
Villa are maintaining their normal stance of refusing to comment on transfer speculation.
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