The listing in London or Hong Kong could be the first in a string of sales from a privatisation programme in Central Asia's biggest economy. Kazakhtelecom, which already trades on the Almaty bourse, will also be listed on the new Astana exchange.
Oil-rich Kazakhstan launched its privatisation drive with the goal of reducing the state's role in the economy by 2021.
VTB and JP Morgan declined to comment. The Kazakh sovereign wealth fund Samruk-Kazyna, which owns 52 percent of the firm, and Kazakhtelecom did not respond to requests for comment.
One source said he expected the Astana bourse, which is due to open in July, to be the "driving force" for the new listing.
Kazakhtelecom, which Thomson Reuters data shows has a market capitalisation of 309.7 billion tenge ($944.32 million), has a 51 percent stake in a local mobile operator co-owned by Tele2 and made a bid for Kcell, another Kazakh mobile firm.
Separately, two banking sources said Kazakhstan's state uranium miner Kazatomprom had delayed its plans to list in London this year due to falling uranium prices, used to power nuclear reactors.
In 2017, Kazatomprom hired JP Morgan as its lead adviser on the flotation.
Samruk-Kazyna, which has holdings worth $67 billion, plans to reduce its investments in Air Astana, Kazatomprom, oil company KazMunayGaz (KMG) and other assets.