She seems to have had the popularity, intellect and backing to at least consider it. Was it something that was ever discussed at the time?
Eleanor Roosevelt had been pressured to run for some form of office after she left the White House following the death of FDR. I don't think it would be hard to say that she felt she had no purpose being in public life after her husband's death, which she discussed in her aptly and somewhat sadly named autobiography, On My Own.
In 1946, she penned an piece in Look Magazine titled Why I Do Not Choose to Run, where she detailed reasons for not running, including her age and lack of spirit to run a campaign, among other things.
Sources: Roosevelt, Eleanor On My Own, Why I Do Not Choose to Run
The Eleanor Roosevelt Papers Project Why did Eleanor Roosevelt refuse to run for office?