The Jeopardy! host was taken to the Cedars-Sinai Medical Centre in Los Angeles following the scare on Saturday (June 23).
Sony Pictures Television, which produces the long-running quiz show, has now issued an update confirming that the 71-year-old is still undergoing tests from doctors but is hoping to return home soon.
The statement said that Trebek is "up and about and in good spirits", adding: "He has been moved to a regular room today and looks forward to returning home as soon as his doctors give their approval."
Trebek, who suffered a minor heart attack in 2007, admitted earlier this year that he had been thinking of retiring from Jeopardy!, which he has presented since 1984.
However, the presenter is still expected to return to the gameshow when it returns for its 29th season in July.