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.
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: