However, if either of them take up Big Brother's offer they will have to walk out of the reality show.
The decision will be made at the end of this week's White Room task, which airs tonight at 9pm on Channel 5.
The housemate who is left behind will automatically get a pass to the final as the winner of the White Room challenge. If neither Conor or Luke decide to take the cash, there will be a twist to find out who wins the White Room task.
The weekly eviction will go ahead as normal tonight with Deana Uppal, Ashleigh Hughes, Becky Hannon and Luke Anderson battling it out in the public vote.
Big Brother continues daily on Channel 5.
[Big Brother Day 59 - In Pictures]