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The pair were together at Claire's home when friends went to visit her recently and they fuelled suspicions by acting strangely.
A source told the Daily Star Sunday: "It was strange to see Lee's car outside. Claire was a bit flustered and Lee was stumbling over his words. We're not sure what they were doing."
Meanwhile, insiders on the series have revealed that Claire clashed constantly with rival contestant Sara Dhada when they shared a room together at the Apprentice house.
One mole said: "They had some almighty bust-ups which left Sara really upset."
A BBC spokesperson confirmed: "There were clashes between Claire and Sara. But things were resolved."
Young, McQueen, Alex Wotherspoon and Helene Speight will be seen competing for a job with Sir Alan Sugar in the show's final on Wednesday night.
