"I have an open mind," the Congress leader said, adding that if the family members insist on a CBI investigation, the state could think about it.
"This is an organised crime, but let the police look into it," he said, adding, "I have instructed the police to take the case seriously."
"Similar weapons were used in M M Kalburgi, Govind Pansare and Narendra Dabholkar's killings, but we can't link anything yet," Siddaramaiah said.
"Two persons had written something against Gauri on Facebook and the police is investigating it," the Chief Minister said.
Earlier, Deputy Commissioner of Police (West) MN Anucheth told IANS: "Three special teams were set up to crack the case. They are on the lookout for the suspected assailants. We are tracking the movement of people and vehicles at check posts and inter-state borders."
"We have alerted our counterparts in the neighbouring states of Andhra Pradesh, Maharashtra and Tamil Nadu as well," said Anucheth.
Lankesh, 55, was shot dead by three unidentified men who fired seven bullets at her when she returned home from her office in the city. Two hit her in the chest and one in the forehead.
She was the editor of popular Kannada tabloid "Gauri Lankesh Patrike".
A prominent Left thinker and a staunch critic of Hindutva politics, Lankesh was convicted in November 2016 in a defamation case filed by Bharatiya Janata Party lawmaker Pralhad Joshi. She was out on bail pending appeal.
The manner in which Lankesh was shot dead was reminiscent of the way Kannada progressive thinker and researcher M M Kalburgi was killed in August 2015 at his residence in Dharwad in the state's northwest region, about 400km from Bengaluru.
Activist Narendra Dabholkar, who was at the forefront of a campaign to persuade the Maharashtra government to pass an anti-superstition and black magic bill, was shot dead by unknown assailants in August 2013.
Dabholkar was found dead in a pool of blood at Omkareshwar bridge in Pune. He was also the editor of Sadhana magazine which was devoted to the propagation of progressive thought.
Senior Communist leader Govind Pansare was shot and killed in February 2015. Two men on a motorcycle shot five times at Pansare and his wife from close range outside their house. His wife survived but Pansare succumbed to his injuries.
Lankesh, Kalburgi, Dabholkar and Pansare -- all were known critics of the right wing forces.
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