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Seeing how its initial bid of $132.50 per share ($37.3 billion) for Time Warner Cable Inc. (NYSE: TWC) produced an immediate rejection, cable operator Charter Communications Inc. (NASDAQ: CHTR) is reported to be considering sweetening its offer to somewhere in the low $140s.

According to an exclusive report from Reuters, people familiar with the matter say that Charter has been discussing a price of $142.50, likely as a result of conversations with existing Time Warner shareholders. Time Warner has said that it will not consider any offer at less than $160 a share, but some of the company’s large shareholders could do some arm-twisting to get the company to look at a lower bid.

The third player in this game is Comcast Corp. (NASDAQ: CMCSA), which is said to have agreed to purchase some of Time Warner’s assets from Charter if that company can make the acquisition. Comcast is interested in Time Warner’s cable operations in New York City and parts of New England.

As total cable subscriber numbers decline, size becomes a paramount concern among cable operators. Comcast and Time Warner are numbers one and two in subscriber numbers, and Time Warner has let it be known that it would prefer a combination with Comcast rather than a deal with Charter. Regulatory approval of such a deal would be more difficult, unless a third party — say, Charter — were involved and Time Warner’s assets could be split up before a deal is approved.

In general, a three-way deal among Charter, Time Warner and Comcast could have an easier path through the regulatory process. Provided that Charter can get its bid up to $142.50, or perhaps even $145 a share, there is not a lot of reason for Time Warner to continue resisting. Unless the idea of being bought out by a smaller rival offends some egos.

Shares of Time Warner traded up about 2.3% in Monday’s premarket, at $136.30 in a 52-week range of $84.57 to $139.85. Shares of Charter and Comcast were inactive Monday morning.