The other two bidders are Singapore Telecommunications and India's Reliance Infocomm.
The interest by big names in the Sri Lankan market was indicative of the "desperation" of operators to secure new markets, an industry source said.
"There are only a few assets in markets with low mobile penetration which are for sale and this explains why even a fifth licence in a country like Sri Lanka will be pursued," the source said.
The Edge said that despite the violence in the country, Sri Lanka had the potential for growth.
At the end of 2005 it had 3.3 million mobile phone users with a penetration rate of 17.3 percent but it lacks landline capacity, making mobile services more attractive.
Other mobile operators operating in Sri Lanka are Dialog Telecom in which Telekom Malaysia has a 87.7 percent stake, Celltel Lanka, Hutchinson and Mobitel.
"If Maxis succeeds in securing the Sri Lankan licence, it could derive some synergies from its neighbouring Indian operations under Aircel Ltd," the Edge said.
Aircel recently launched coverage in West Bengal, Orissa, Assam and Jammu and Kashmir.
It expects to launch other coverage areas in Bihar, Himachal Pradesh, Madhya Pradesh and Uttar Pradesh.Maxis, controlled by tycoon Ananda Krishnan, is Malaysia's top telecommunications company with nearly eight million subscribers.