"I'm not convinced it's time to buy aggressively yet," he told CNBC. "The market is looking for growth in the 5 to 7 percent range...probably not consistent with the slower economic scenario."
Fuller says both stocks took a hit after being driven sharply higher by merger speculation. He thinks the hits may keep on coming for a while.
"They probably have another leg down in terms of earnings estimates," he said. "I'd rather buy these stocks after that leg down than before it. Valuations are definitely looking more interesting here. I'd just rather see that move first."
Fuller and his family own shares of Marriott.