Gunners boss Mikel Arteta has made Rice one of his main transfer targets, with suggestions that a deal was close.
However, it is understood the initial offer for the 24-year-old has left the Hammers unimpressed as it contains a number of clauses.
Sources at West Ham do expect further communication from Arsenal, although they are also anticipating an offer from Manchester City. City are refusing to comment on potential interest in Rice.
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