CBS News Correspondent Kimberly Dozier says British boxing authorities could cancel the bout because Tyson is on drugs, even though the drugs in question are quite legal.
The former heavyweight champion is taking a prescription drug to balance chemicals in his brain, according to co-trainer Jay Bright.
Bright said Tyson began taking the medication on the advice of doctors linked to the Nevada State Athletic Commission.
The British Boxing Board of Control's chief medical officer, Adrian Whiteson, recently expressed concern about reports that Tyson might have been taking tranquilizers.
"The doctors in Nevada felt it might help," Bright was quoted as saying today in the Daily Telegraph. "It was a doctor who suggested it - and it's funny that people over there say they don't want him to take it.
"What happens is the medication balances the chemicals out, and when something happens, he reacts properly and doesn't lose his temper."
Bright said Tyson's handlers have also been working with the fighter to help him control himself and remain calm in the ring.
Tyson, who has been training in Phoenix, is scheduled to arrive in London next Wednesday before heading to Glasgow a few days before the Savarese fight. A sellout crowd of 60,000 is expected at Glasgow's Hamden Park stadium.
It will be Tyson's second fight in Britain in five months. In January, he knocked out Julius Francis in the second round in Manchester, England.
"Tyson is ready to go," Bright said. "He is ready to vaporize anybody who is in front of him."