"I'd like to know where you heard that and then I'll give you my answer," he said, when asked about sparring with Fa.
Eventually, he said: "Yes, I sparred with him. I really appreciated the time he took to spar with me. It went well.
"It wasn't necessarily a secret, but also I wasn't necessarily wanting to let everyone know."
For his part, Parker said: "I don't think you can gain a lot sparring this close to the fight."
Not surprisingly Parker was a lot more at ease in the more familiar surroundings, saying he had been relaxing on PlayStation after his training sessions - his favourite games are Black Ops and Streetfighter.
Asked whether he was prepared to be hurt after coming through his previous 18 professional fights undefeated, Parker said: "I have a lot of respect for Carlos and what he's done in his career. He's been in the ring with some big names. The plan is not to get hit, but with boxing, if you have a guy like Carlos who's prepared to give me a good fight, who is confident in himself and who has trained the house down, then you're definitely going to take some punches.
"I'm definitely excited about fighting someone like Carlos, who is going to be a good name on my record if I beat him."
Takam said of Parker: "With time, he's going to be one of the best. But right now I'm here to win."