The actor was said to be upset by images of his wife with the boxer following his recent unanimous points victory over Marcos Maidana in Las Vegas.
However, Reid told today's Star: "It was good to have the missus back after her trip to the US to watch Amir Khan's boxing match. It was not nice to read the stories on her while she was away, though. I don't believe them.
"Everything is still good with us. The only thing I was jealous of was not getting to see the fight! But I had my own things to do so I had to stay here."
Of his own recently-acquired US accent, he added: "I keep talking in an American accent at the moment as I am practising for an audition.
"It is for the role of an American soldier in a sci-fi movie. Everyone probably thinks I am being weird, but it’s all in the name of work!"