The former West Indies spinner, who took charge of Kenya in January 2006 with the task of preparing the national side for the ongoing World Cup in the Caribbean, stayed behind when the team returned home on Tuesday.
Kenya, semi-finalists in the last tournament in 2003, were eliminated after losing two Group C matches against New Zealand and England and registering only one win over Canada in their opening match.
Cricket Kenya chairman Samir Inamdar said his board would meet to discuss an extension for Harper, who is on vacation in his native Guyana, with the aim of taking the team to the Twenty20 World Cup in South Africa in September.
"The coach has done very well and we are very grateful to him for having created a unified team," said Inamdar. "The team would have done better in the West Indies if it were not for some minor mistakes including giving away easy wickets.
"But we were not humiliated. We will ask Harper about his views before we make the final decision," Inamdar said.
As well as the coach, the national team players are expected to be put under formal contracts for the first time in four years following the arrival of a new sponsor.