Viacom is preparing a counteroffer after spurning an initial approach from CBS.

Viacom Inc. (VIAB - Get Report) has rejected CBS Corp.'s (CBS - Get Report) initial bid and is preparing a counteroffer, according to a source close to the situation. The source said Viacom could counter CBS' bid this week.

Viacom shares closed up 3.9% on Wednesday, April 4, at $30.57, giving it a market capitalization of $13.2 billion. With $394 million in cash and $10.2 billion in debt as of Dec. 31, the owner of Paramount Pictures, MTV and Nickelodeon has an enterprise value of roughly $23 billion.

Reports on Wednesday put the rejected offer at 0.55 CBS shares per Viacom share, which translated to $29.07 at Tuesday's closing price for CBS of $52.86. Viacom shares ended Tuesday at $29.42, meaning the reported initial offer came at a discount to market value.

CBS shares also headed higher on Wednesday, to $53.79. Its market cap is $19.75 billion.

Sources told CNBC and Reuters that Viacom would seek more than 0.62 CBS shares per Viacom share. The target plans to point to potential cost synergies of more than $1 billion as justification for a market premium, the reports said.

Previous analyst reports have speculated that a deal would come at a premium to Viacom's share price, with RBC Capital Markets analysts in March citing factors such as a desire for control over price, the potential to avoid shareholder lawsuits and compensating for Viacom's turnaround efforts.

The two sides also reportedly differ on who would fall behind CBS chief executive and chairman Leslie Moonves in leadership of the combined entity: Viacom CEO Bob Bakish or CBS COO Joseph Ianniello. National Amusements Inc., the controlling shareholder in both CBS and Viacom, favors Bakish, the reports said.

CBS and Viacom representatives declined comment.

The companies on Feb. 1 announced the formation of special committees of their boards of directors to evaluate a potential merger. The companies cautioned there was no guarantee they would reach a deal or of the terms of any transaction.

Theater chain National Amusements has expressed support for the process and in the past has pushed for CBS and Viacom to consider a merger. In September 2016, National Amusements approached both boards, only to conclude in December that the time for a merger was not right.

CBS and Viacom were housed under the same corporate roof until Dec. 31, 2005, when Viacom was spun out of the television broadcaster.

When Sumner Redstone of National Amusements announced Viacom's $37.3 billion purchase of CBS in 2000, it was the largest media deal ever.

He envisioned a global media powerhouse, but just five years later the amalgamation of cable, broadcast and film production companies had become too complicated. Viacom spun off CBS to make the companies easier for investors to value and invest in and for management to run.