Dublin's Aviva Stadium will host the fixture on 15 November, with Poland providing further competition in Poznan four days later.
The Republic are currently in the process of identifying a new permanent manager following Giovanni Trapattoni's departure in September.
Under-21 boss Noel King took charge of the final two World Cup qualifiers against Germany and Kazakhstan earlier this month.
Martin O'Neill remains the preferred candidate, although Mick McCarthy and Roy
Keane are understood to be serious contenders.
The Republic started and finished the campaign with victory over the Kazakhs but poor results inbetween - namely two defeats in five days last month - ended their hopes of making the finals.