The phrase 'question presents itself' is correct and can be used in written English
You can use it to suggest that a question has come up that needs to be considered. For example, "Given the circumstances, a question presents itself: What is the best course of action here?"
The inevitable question presents itself.
And if you're listening closely, the question presents itself.
And, with every news report that arrives, the same unanswered question presents itself.
So now that you're aware of the situation, a question presents itself: Is long-term care insurance doomed?
Which raises a question:[I]f you take labor's decline as a given, then another question presents itself: How do you limit the resulting corporate power over elections and legislators?
When Simin and Nader part, and Simin leaves to live with her mother, an instant question presents itself – with no wife in the picture, who is to do the woman's work?
Amid the week of celebration, one question presented itself: what now?
A similar question presented itself in downtown Brooklyn, where a row of 14 new town houses went on sale in 2005 in a project called "14 Town Houses".
As we sat on a cold, foggy afternoon, playing a 1983 British edition of "Trivial Pursuit," the question presented itself: What is the name of a person who studies the weather?
AG: Well, we began with a very binary question on the show, which is, "Is he or isn't he? Has he or hasn't he been turned?" And then, as we moved further into the season, a much more interesting question presented itself, which is, "If he has been turned, will he go through with it?" And that was really the question that burned through the second half of the season.
The question presented itself as to whether the 96FASP plate with the relatively low MWCO of 10 kDa and limited centrifugal forces applied in a plate-adapted centrifuge allowed ultrafiltration of high molarity solutions (8 M urea) in a reasonable time frame.
