The petition launched by Ali Abdi under UK-based change.org has 1,985 signatures so far against a target of 2,500.
Abdi, in his petition, said Kenya transformed from dictatorship to a multi-party democracy because of Mr Odinga's efforts.
"Kenyans could have been in the dark without his sacrifices. Raila has also brokered peace initiatives not only in Kenya but the African continent as a whole."
Abdi also cited the recent hand shake with President Kenyatta adding that the Orange Democratic Leader "saved Kenya from turning into a bloody civil war."
Wangari Maathai
The petition has gained traction since its launch a few days ago with several users sharing the link across the globe to nominate the Opposition leader.
In 2004, the late Wangari Maathai, a Kenyan environmentalist, became the first African woman to receive the award for her contribution to sustainable development, democracy and peace.
A nomination for the Nobel Peace Prize may be submitted by any person who meets the nomination criteria.
There are 330 candidates for the Nobel Peace Prize for 2018 out of which 216 are individuals and 114 are organizations.