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The actress made her debut in the show last week as Morgan, an intern working with Alex (Justin Chambers).
Morgan, who was pregnant, ended up having heart trouble and the doctors were forced to deliver her baby prematurely.
Fuller has now revealed that the other doctors will believe that something is going on between Morgan and Alex.
"Karev's really oblivious to the fact that everyone's running round the hospital that they're doing it," she told TV Guide.
"They're spending so much time together and they bicker and banter like two kindergarten kids who have a crush on each other, so he begins to realise that everyone may be right about her being into him."
Grey's Anatomy airs on Thursdays at 9/8c on ABC.
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