The pair had been linked while filming the show but both played down the rumours ahead of the final on Sunday night.
Jessica had said: "Oh, don’t believe everything you read in the papers unless it comes from the horse’s mouth! You’ll have to ask Courtney on that one…but no, we’re just good friends."
But sources insist they are very much are together and are preparing to jet off for a holiday after Christmas.
"It's true, they are seeing one another. And they have booked a holiday, for immediately after Christmas," the source told the Daily Mail newspaper. "The relationship is in the early stages though. They are going to give it a go and take it from there."
Speaking to The Sun newspaper, Jessica confirmed the report and admitted that they were in fact together while on The Apprentice.
"To be fair we did have a romance on the show. It is early days now. We are seeing how everything goes. He is a good-looking lad," she told the tabloid. "He is charming and considerate.
"We do like each other though and we are just going to take things slowly."
Jessica made it as far as the interview stages on this year's series while Courtney finished as runner up, with Alana Spencer winning Lord Sugar's £250,000 investment on Sunday night.
The Apprentice will return to BBC One next year for a thirteenth series.