It's not shown exactly, but there are subtle clues throughout the movie that he might be suspecting something. For example, when he tries to surprise her for their anniversary and sees her taking off from their apartment when he thought she was staying home. Then, he waits all night for her, but she doesn't return until morning. Pretty strong clue that something might be going on. He may also have noticed changes in her behavior when she was around Almásy, even if he didn't suspect him at first.