There are suggestions further up this thread that Edward VIII was mooted as a possibility, but he and Olga barely knew one another, having only met during the 1909 visit (and perhaps when Nicholas, Alexandra and the infant Olga went to Balmoral in 1896).
In any case, there was an age issue, since Edward was only 20 (just) in August 1914 (born June 1994), so by the standards of the time too young for marriage (for a man). The youngest bridegrooms I know of in that period were Alfonso XIII of Spain and Charles Edward of Coburg, who were both aged 21 and, as posthumous sons, had a peculiar need to produce heirs quickly. There was still more of an age issue with George VI, who was still only 18 in August 1914 (born 14 December 1895). Five years later, say, there would have been no age issue with the two princes, but Olga would be close to being on the shelf.
Carol of Rumania was 21 in 1914, but still rather young for marriage.
Ann