Somali civilians and military officials say al-Shabab militants have been exiting Kismayo in recent days, fearing an impending onslaught by Somali forces, African Union troops and allied militaries.
Some fighters said to be remaining behind may continue to pose a serious threat.
Kenyan military spokesman Colonel Cyrus Oguna says ground troops are about 50 kilometers from Kismayo, and advancing from the northwest and the south, backed by navy and air forces.
Port Kismayo, Somalia
He says reports of al-Shabab fleeing the city are only “partly true,” adding that some elements may be planning to stay behind to snipe at allied forces when they enter the city.
2006: Launches insurgency to topple Somali government, impose Islamic law
2008: U.S. declares al-Shabab a foreign terrorist organization
2009: Seizes control of parts of Mogadishu, Kismayo
2010: Expands control across central and southern Somalia; carries out deadly bombings in Kampala, Uganda in first attack outside Somali
2011: Blocks drought/famine aid from areas under its control
2011: East African leaders declare al-Shabab a regional threat, Ethiopian, Kenyan troops enter Somalia to pursue the group, which is driven out of Mogadishu
2012: Declares itself an al-Qaida ally, loses ground in Somalia, troops advance on the group's stronghold Kismayo
But Oguna says he does not expect a tough fight against these remnants.
“We do not anticipate stiff resistance as we get into the city because the main commanders are leaving," said Oguna. "We do not expect the junior forces to fight without their commanders. So we expect minimal resistance as we get to Kismayo.”
He also says the militants have dismantled a radio transmitter in Kismayo, a sign that they are no longer using the city as a base for operations.
"The radio that al-Shabab has been using to broadcast most of their statements is called Radio Andalus and the transmitter has been brought down," Oguna said. "So we reckon that they have removed it to take it to another location, possibly Jilib."
Jilib is among the other small towns in central Somalia where al-Shabab commanders are believed to be heading to avoid the military assault.
Al-Shabab has denied its fighters are retreating from Kismayo and claim to be defending their positions in the city.
Kismayo is one of the largest remaining strongholds of the al-Qaida linked group, which has used the town's seaport to funnel in weapons and other supplies to support their insurgency.
The militants were driven out of the capital, Mogadishu, by African Union forces in August last year. But the remnants that have remained behind in the capital continue to pose a serious threat by carrying out suicide bombings and other small scale, targeted attacks.