The former Strictly Come Dancing contestant met the Chelsea player at the Pride of Britain Awards last month, the Sunday Mirror claims.
A source told the newspaper: "Frank thinks she's a great girl and incredibly sexy. He wants to spend some time getting to know her better. He thinks she's special.
"But Christine's taking it slow and she's not rushing into a full-blown relationship. They're blissfully happy."
The One Show presenter was snapped leaving Lampard's house in the early hours of the morning this weekend.
According to the newspaper, she had been comforting the star after he was forced to return home early from Qatar with a thigh injury sustained during training for yesterday's match between Brazil and England.