In his final submissions, Odumbe's lawyer Ishan Kapila argued that prosecution evidence was based on hearsay.
The charge centred on allegations that the former Kenyan skipper "received money, benefit or other reward which could bring him or the game into disrepute."
The defence has until August 6 to provide final written submissions to presiding adjudicator, former Zimbabwean Supreme Court Judge Ahmed Ebrahim, and the prosecution will be given three days to respond to these submissions.
Ebrahim will then consider the evidence and determine whether the charge levelled against Odumbe is proven. A judgement is likely to be delivered in the week commencing August 16.
Odumbe, who was named in the Kenyan squad to play the opening three-dayer against Pakistan 'A' in Nairobi on Saturday, could face a minimum two-year suspension or a life ban, as well as a fine, if found guilty.