Sikorski confirmed the timing in an interview published Monday in the daily newspaper Dziennik.
"The program is being finalized, but its likely that the (Polish) prime minister (Donald Tusk) and the secretary of state will make a political declaration, and the ministers will sign the technical deal on the base," Sikorski added.
Polish government officials were not immediately available for comment.
On Sunday, Rice had told the U.S. network Fox News that she was "going to Poland to sign a missile defense agreement in the next couple of days".
Moscow is deeply opposed to the missile plan, and the deal signing comes amid a spike in tensions between Washington and its allies over Russia’s conflict with pro-Western Georgia.
Washington plans to base 10 interceptor missiles in Poland plus a radar facility in the neighboring Czech Republic by 2011-2013 to complete a system already in place in the United States, Greenland and Britain.
U.S. and Polish negotiators inked a preliminary deal in Warsaw last Thursday, capping 15 months of grinding negotiations. Washington and Prague had already sealed the radar deal in July.
Washington insists the shield -- endorsed by all 26 NATO member states earlier this year -- is to fend off potential missile attacks by what it calls "rogue states", a phrase regarded as including Iran.
The plan, however, has become a major source of tension with Moscow, which considers it a security threat designed to undermine Russia’s nuclear deterrent. Moscow has warned of retaliation against the Poles and Czechs.
Warsaw and Prague have had rocky relations with Moscow since they broke free from the crumbling communist bloc in 1989, and ties have worsened since they joined NATO in 1999 and the European Union in 2004.