Truman does not explicitly say what role he envisions for the UN in this speech. However, it is pretty clear from what he does say that he does not believe that the UN can be of any great help in the current situation.
Truman mentions the UN a number of times in the speech, but always in a context that suggests he does not think it will be useful. He says at one point, for example, that the UN is "not in a position to extend help of the kind needed." Later on he says that the UN was founded to make it possible for countries to have "lasting freedom and independence" but then goes on to say that it is the US that must help keep people free.
From these sorts of statements, it is clear that Truman does not see a major role for the UN.