Don't Look Now by by Henry Kuttner. I read it in the anthology Tales from the Spaceport Bar, though it has been collected many times. It has been asked about before in the question Looking for a short story about a man at a bar who thinks aliens are hiding at the edge of vision
It starts:
The man in the brown suit was looking at himself in the mirror behind the bar. The reflection seemed to interest him even more deeply than the drink between his hands. He was paying only perfunctory attention to Lyman’s attempts at conversation. This had been going on for perhaps fifteen minutes before he finally lifted his glass and took a deep swallow.
“Don’t look now,” Lyman said.
The brown-suited man slid his eyes sidewise toward Lyman, tilted his glass higher, and took another swig. Ice cubes slipped down toward his mouth. He put the glass back on the red-brown wood and signaled for a refill. Finally he took a deep breath and looked at Lyman.
“Don’t look at what?” he asked.
“There was one sitting right beside you,” Lyman said, blinking rather glazed eyes. “He just went out. You mean you couldn’t see him?”
The man in the brown suit is the reporter and Lyman is the Martian. It ends:
Lyman sat there. Between two wrinkles in his forehead there was a stir and a flicker of lashes unfurling. The third eye opened slowly and looked after the man in brown.
