Listen,
When it comes right down to it, if a person is aware that both partners in a friendship like each other, but won'd do anything about it, then that person is waiting for the other person to take the first step in honesty. No matter who does the asking, this is already a red-flag for the relationship. Somebody should just fess-up and ask.
Also, about who should ask first, lets take a little history lesson.
For centuries, the effort was made on the part of the woman and her family. A woman was seen as a burder by her family, so they wanted her to get married. The woman wanted to be married to the most financially and socially well-established man she could get, so she would dress herself-up, and go through other gyrations to maker herself seem more appealing. Then, if the man like her, he would simply ask her Father, or nearest male relative, if the could be married, and the father would or would not consent.
Then, Eleanor or Aquataine came around (She was the mother of King Richard II of England). She had no surviving male relatives by the time she was ready to marry. But, she did have a rather significant kingdom as a dowry. So, Eleanor did not have to do anything. Men showed up from all over the world to win her affection. Why? Money and power. At any rate, this was the beggining of the new European courtly love tradition. From that time, until about the romantic age (and in most places, beyond that), marriage was a financial transaction that was begun by the male party. He would woo the woman. Once he had one her affections (whatever was the way to her heart: art, looks, money), he would go to her family and ask to marry the daughter. The family would look at the man's credentials (annual income, quarterings, class, investments, lands, ancestry and other matters of heraldry) and make a decision. Sometimes men had to do a little bit more to prove themselves. Incidentally, until the twentieth century, not a single person of nobility ever married a member of the common class--Sorry, Cinderella.
Then the romantic age came around. It was common up to this point, and beyond, for courtly spouses to have extra-marital lovers. However, during the romantic period, much of the way people interracted with each other changed. Things had been changing quite a bit up to this point, but men and women, at this time, were not always letting money be the only issue. Consider Jane Austen's (who never married) Pride and Prejudice. There is obviously some affection between Lizzie and Darcey. So, we like that they are to make a match. But, when Jane asks Lizzie when she first knew she [Lizzie] loved Darcey (note that "love" is even an issue), Lizzie explains that it was when she saw Mr. Darcey's estate.
Now, we live in an America, and indeed, much of the world is like this, where rank and nobility are non-issues. In fact, it is considerred noble when people marry for love, forsaking money or prospects. For this way, there is no answer. Although, I think it is an excercise of honesty when an affectionate party makes his or her affections known. To withold affections because of principle or shame is, in my opinion, cruel.