Oliech, who plays for French Ligue 1 side AJ Auxerre and is the captain of the east African country's national team, Harambee Stars, pulled out of the team preparing for a World Cup qualifier against Togo on June 16.
Oliech is demanding an unspecified amount of money because his picture was used by sponsors of the local federation in a billboard advertisement.
The sponsors, East African Breweries Limited, and the Football Kenya Federation (FKF) have said the player is not entitled to any payment as the terms of the sponsorship did not include that provision.
"The contract allowed the sponsors to use the national team pictures for promotional purposes. But we are now renegotiating to come up with a win-win situation for the players and the sponsors," said FKF Chairman Sam Nyamweya.
FIFA's Director of Legal Affairs, Marco Villiger, said in a statement to FKF that the player was liable for disciplinary action if he snubbed a national team call-up.
"As a general rule, every player registered with a club is obliged to respond affirmatively when called up by the association he is eligible to represent on the basis of his nationality to play for one of its representative teams," Villiger said in a statement on Wednesday.
"Violations of the provisions set forth in Annexe 1 of the FIFA rule may lead to the imposition of disciplinary measures."
Another Kenyan top player MacDonald Mariga, who plays for Italian Serie A side Parma, has fallen out with the Kenyan federation over the unpaid reimbursement of more than one million shillings ($12,000) for air travel he used to join up with the national side.
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