The couple, who shot to fame on MTV's The Hills, will enter the house when the new series starts on January 3, according to the Daily Star.
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Steps singer Claire Richards is also the latest name to be linked to the show, joining other rumoured celebrities including Katie Price and X Factor's Rylan Clark.
Meat Loaf and Coronation Street duo Bruce Jones and Wendi Peters have also been tipped to enter the house.
A petition has been launched to stop Justin Lee Collins entering Celebrity Big Brother, after he was apparently approached for the show. He was convicted of harassing his ex-girlfriend in October.
Montag previously participated in the US version of I'm a Celebrity... Get Me out of Here! with Pratt. She recently told how she has blown $1 million since The Hills finished.
Producers are said to be planning a Swedish ice hotel theme for this year's house, with a real igloo being built in the garden.
Photo gallery - Celebrity Big Brother rumoured housemates:
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