The X Factor winner and Xtra Factor presenter are said to have spent several hours together at a London bar on Thursday night (December 13).
The pair were allegedly seen flirting with each other on the X Factor wrap party on Tuesday, before having their own night out two days later, reports The Mirror.
A source claimed: "James built up a reputation as a ladies' man over the series and made no secret of the fact he was enjoying all the female attention he was getting.
"But while he has been playing the field, he has always had feelings for Caroline. She made it clear nothing could happen while the show was still on, but as the weeks went by they got closer and closer.
"At the wrap party on Tuesday - which was held at the Hippodrome Casino in London - they spent almost the entire evening together, and there was a lot of flirting. They left separately but arranged to meet again."
The source continued: "On Thursday they went to the Groucho Club together and spent four hours chatting and drinking. They looked like they were really close."
The couple were reportedly joined by David Beckham, James Corden and Jason Statham on Thursday, but the source added: "They were alone the rest of the time.
"Again, they went home separately but they had a great evening and really enjoyed each other's company. There could definitely be a future between them."
James Arthur was previously quoted as saying: "I think Caroline Flack is beautiful. Maybe we'll see in the future. Things like this have to develop."
Meanwhile, Flack said of Arthur: "He has this way of making you touch your hair and go all girly when he gives you compliments. He's just very charming.
"And he is like that with a lot of girls. I don't think it's just me, because he's very good at it."
However, Flack's spokesperson has denied that the pair are dating, saying: "It's definitely not true and it won't be changing anytime soon."
Caroline Flack was previously said to have turned down an offer of a date from Arthur back in late October.
The TV presenter has also dated former X Factor contestant Harry Styles of One Direction.
Watch the music video for James Arthur's 'Impossible' below:
Photo gallery - The X Factor Jahmene vs James:
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