Official sources said that formal notification for their appointment will be issued by Rashtrapati Bhavan soon.
Prime Minister Narendra Modi and home minister Rajnath Singh are said to have discussed the issue two days ago and shortlisted the names, they said.
Veteran BJP leader Naik said in Mumbai that the party leadership had approached him to accept the post of Governor of Uttar Pradesh, to which he agreed.
"I was asked by my party to accept the position of the governor of UP and I said yes. It is a challenging job and I am accustomed to doing challenging jobs," Naik told PTI.
If appointed, Naik will replace BL Joshi, who demitted office after the NDA government decided to replace Governors appointed during the previous UPA tenure.
Following the change of guard at the Centre and the new regime's pressure, five Governors have already resigned. They are BL Joshi (Uttar Pradesh), MK Narayanan (West Bengal), Shekhar Dutt (Chhattisgarh), Ashwani Kumar (Nagaland) and BV Wanchoo (Goa).
Two governors - HR Bhardwaj (Karnataka) and Devanand Konwar (Tripura) - retired late last month, while a few days ago, Lt Governor of Puducherry Virendra Kataria was sacked by the government.