The former Bihar governor will be accompanied by senior BJP leader and Union Minister Nitin Gadkari in the Uttar Pradesh leg of the tour.
BJP sources said Mr Kovind, 71, would travel to the bigger states and interact with electoral college members from more than one state.
He would also discuss the issue with MPs and MLAs of the parties which have announced their support to him.
Lok Sabha and Rajya Sabha members besides MLAs from all state assemblies comprise the electoral college, totalling 10,98,882 votes.
The vote value of a member of the Lok Sabha or the Rajya Sabha is 708, while that of an MLA would depend on the population of the state he or she represents.
State BJP leaders may reach out to opposition parties as well and ask them to attend the meetings to be addressed by Mr Kovind
The complete itinerary of Mr Kovind's travel is still being finalised as it will also depend on the availability of state leaders, including NDA chief ministers and others supporting him, sources said.
After filing his nomination, Mr Kovind reached out to the opposition by asserting that the president's office was above party politics and that he did not belong to a party.
"Since I became the governor I do not belong to any political party," the former head of the BJP's Dalit Morcha said.
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