This is not a conclusive argument that Eleanor Roosevelt never said this - it is practically impossible to prove that someone never made a particular argument. Further, I have not spent much time reading biographies or other histories about her.
However, there is some circumstantial evidence to suggest that this was not her (publicly espoused) point of view.
- On September 2, 1939, when Germany invaded Poland, she wrote in her syndicated newspaper column, "My Day":
As I listened to Hitler's speech, this letter kept returning to my mind. How can you feel kindly toward a man who tells you that German minorities have been brutally treated, first in Czechoslovakia and then in Danzig, but that never can Germany be accused of being unfair to a minority? I have seen evidence with my own eyes of what this same man has done to people belonging to a minority group--not only Jews, but Christians, who have long been German citizens.
In general, the tone of her article is strongly hostile to Hitler, but sympathetic to both the German people and the minorities who suffered under Hitler.
- On August 13, 1943, she published another column.
In it, she takes a balanced view of the Jewish people, but identifies that they have suffered strong persecution, and calls for going to their support:
The Jews are like all the other people of the world. There are able people among them, there are courageous people among them, there are people of extraordinary intellectual ability along many lines. There are people of extraordinary integrity and people of great beauty and great charm.
On the other hand, largely because of environment and economic conditions, there are people among them who cringe, who are dishonest, who try to take advantage of their neighbors, who are aggressive and unattractive. In other words, they are a cross-section of the human race, just as is every other nationality and every other religious group.
But good or bad, they have suffered in Europe as has no other group. The percentage killed among them in the past few years far exceeds the losses among any of the United Nations in the battles which have been fought throughout the war.
[...]
I do not know what we can do to save the Jews in Europe and to find them homes, but I know that we will be the sufferers if we let great wrongs occur without exerting ourselves to correct them.
There is evidence that her point of view had been different before the war:
This paper claims she had revealed an "inbred dislike" of Jews, based on her correspondence complaining about a party (seems a bit flimsy to me), but goes on to explain how much support she gave (sometimes behind the scenes) for pro-Jewish initiatives during and in the lead up to the war.
This book agrees that Eleanor Roosevelt's view of Jews changed over time (page 32), until by 1952, she was supporting Israel and being the World Patron of Youth Aliyah (page 35).
Conclusion
No matter what her earlier views, by the time World War II began, Eleanor Roosevelt was a vocal supporter of the Jewish people, and continued to act openly and behind the scenes in their aid, up until her death.
That doesn't prove she never made such an argument, but it is clear that the argument wasn't consistent with her sustained actions and public opinions.
