The London-based International Cricket Council's (ICC's) anti-corruption unit, chaired by Lord Condon, is reported to have appointed Zimbabwe's Justice Ahmed Ebrahim to preside over the hearing of Odumbe's case in May.
The hearing will involve the ICC and the Kenya Cricket Association (KCA).
The ICC said that if found guilty, Odumbe, who captained Kenya to their first-ever World Cup appearance in the Indian subcontinent in 1996, may face a life ban.
However, KCA officials and Odumbe said in Nairobi on Friday that they would not comment on the issue until they received clear information from the London-based world cricket governing body.
"My conscience is clear on this," Odumbe said at a Nairobi physiotherapy clinic where he has been seeking treatment for a broken toe he injuried during Kenya's recent tour of the West Indies.
"I see a lot of intimidation in the whole affair, especially where Justice Ahmed Ebrahim is involved. He's the same guy who sent me off during the triangular series in South Africa in October 2001 when he was the match umpire," he said.
Odumbe is considered one of the greatest cricket players ever produced by Kenya. He scored a century in the country's stunning 53-run win over Sri Lanka and hit the winning runs to propel the East African nation to the semi-finals of the World Cup in South Africa last year.
He reached his 207 runs with a sparkling performance in the Caribbean Carib series in January.
Senior KCA official Sharad Ghai said they were treating the inquiry as speulation.
"We knew the ICC's Anti-Corruption Unit would look into the affair, but this is indefinite. They said they would investigate Kenya's win against Sri Lanka. Other investigations against English players have all turned out to be inconclusive," said Ghai, the KCA chairman of cricket committees.