"perceive a problem" is correct and usable in written English.
You can use it when you need to refer to understanding, recognizing, or noticing a problem. For example, "By performing an extensive analysis of the data, I was able to perceive a problem with the process."
I'll admit I didn't perceive a problem with the old roll center, whatever it was.
Labour will ensure councils can reduce the number of, or remove, FOBTs in betting shops if local people perceive a problem in their area".
When we feel the need to help we perceive a problem that we want to alleviate, and its persistence can trigger discomfort, anxiety, anger, and fear.
That way, he said, in his principal role as Goldman's chief financial officer, he can perceive a problem in plenty of time to do something about it.
Their male counterparts perceive a problem, but they tend to dismiss it as resulting from timidity, defensiveness, lack of focus, or excessive emotion.
Michael Parchment, the general manager of Miller Motorcars, a nearby dealership that Mr. Zeeve said provides some of the cars that are speeding by his house, including Maseratis, said he did not perceive a problem regarding his dealership.
President Jiang Zemin has at least sent a hint that he perceives a problem.
And presumably, he said, the board perceives a problem created by baby strollers in the passenger elevators.
Conservative strategists who have perceived a problem in attracting female voters wanted to make sure those potential supporters knew about the new additions.
Upon perceiving a problem, the agent works its way through the tree, performing tests that discriminate among successively smaller subsets of potential faults.
He explains that the process of governing financial activity normally begins when an industry perceives a problem.
