I do have this book and looked through it briefly. In the index it mentions Dmitri visiting/ possibly visiting Alexandra twice before he murder of Rasputin- no other references to Alexandra and Dmitri until after the murder of Rasputin. On p. 463 she writes to Nicholas in April 1916 that Dmitri may show up to visit her, if it doesn't bore him. She says nothing else with regards to Dmitri. Then on p. 471, in August 1916, she writes to Nicholas that Dmitri has visited her, and that his heart is not good like hers, but that it is just the begining of his having this problem, and that it can be cured, if he takes a cure. I couldn't find any other references, although I can look more thoroughly- I checked under Dmitri's entry in the index, and Alexandra's, and Olga's. Felix Yusupov also is quoted from his memoirs on p.471 about the relations between Nicholas and Alexandra and Dmitri prior to the murder of Rasputin. He says that they looked on Dmitri as son, but says nothing about a possible marriage between Olga and Dmitri. What's interesting is page 381, where it quotes from Yusupov's memoirs, saying that both he and Dmitri wanted to marry Irina, but that Irina only wanted to marry Felix, at least that's what Felix says she said after he ( Felix) told Irina that Dmitri had wanted to marry her too. To quote Felix, " Dmitri bowed before a desicion which he realised was final, but our friendship was to suffer and our relations were never the same afterwards." One has to take Felix with a grain of salt though.
Alexandra does mention in this book, p. 453 that she doesn't want Olga marrying Boris, GD Vladimir A and Miechen's son, who was a well known playboy type. She writes to Nicholas that although the ever ambitious Miechen pushed this marriage, she, Alexandra did not think that Olga would ever agree to this marriage, and that she, Alexandra agreed with Olga's inclinations there. Maybe you were thinking of that, but she was writing of Boris, not Dmitri. I do recall a quote/ or something like you remember Sasha18, but it might not come from this book. Maybe the Complete Wartime Correspondence mentions this- I will check it.