Charter Communications Inc. is nearing an agreement with banks to borrow money for a bid for Time Warner Cable Inc., according to people familiar with the situation—a sign that the scrappy cable operator's effort to engineer a combination of the two companies may be moving into high gear.

Charter has held talks with Bank of America Corp., Barclays PLC and Deutsche Bank AG about a multi-billion dollar debt package that would underpin an offer for Time Warner Cable, which has a market capitalization of nearly $35 billion, the...