Cukurova, which controls the country's biggest mobile network Turkcell, is talking to KKR and Texas Pacific Group, the source said.
"Cukurova Group wants to keep a 51 percent stake," he said.
Show TV is valued at at least $800 million and the valuation could easily rise above $1 billion based on a multiple of 12 times earnings, the source said.
Turkcell recently said it received orders from tax offices for the sequestration of the Turkcell assets of Cukurova for 1.68 billion lira ($1.06 billion) due to tax debts.
The source said Cukurova's other units including Digiturk and Genel Enerji may be subject to stake sales to finance the tax debts.