Apple (AAPL - Get Report) CEO Tim Cook told Jim Cramer on Tuesday evening that there have been no settlement discussions between his company and chipmaker Qualcomm (QCOM - Get Report) since last September.

But Qualcomm says that's not the case.

The two companies are locked in a series of patent and licensing disputes around the world having to do with the way that Qualcomm charges for its modem chips and designs.

On CNBC's Mad Money, Cook said that "the truth is, we haven't been in any settlement discussions with them since the third calendar quarter of last year."

In November, however, Qualcomm CEO Steve Mollenkopf told CNBC that the two companies talk regularly and that he was optimistic a resolution to their dispute would be reached in the second half of 2019 and into 2020.

Late on Tuesday, Qualcomm called Cook's latest remarks "misleading" and claimed that since September, "there has been dialogue between the parties at various levels," contrary to what Cook said on Tuesday.

A Qualcomm spokesperson said that "we have been consistent for the last 18 months in making clear that we have, at various times, been in discussions with Apple about a possible resolution to our licensing dispute. We have also stated clearly on several occasions that we believe it will be resolved, one way or the other, in the near future, either through a settlement or court decisions."

Cook elaborated on Tuesday that "the issues that we have with Qualcomm is that they have a policy of no license, no chips. This is, in our view, illegal." Cook continued that "secondly, the obligation to offer their patent portfolio on a fair, reasonable, and nondiscriminatory basis. And they don't do that. They charge exorbitant prices."

Qualcomm shot back against this claim about high prices, noting that "Apple has paid less than $20 per phone for access to Qualcomm's patent portfolio since our business relationship began, while the price of Apple's iPhones has gone up over 200% during the same time."

In late December, a German court granted Qualcomm an injunction banning the sale of certain older iPhones in that country due to the infringement of power management patents. And a week prior to that, a Chinese court granted a similar injunction to Qualcomm in China based on the infringement of software patents. This past Friday, the FTC's suit against Qualcomm for alleged anticompetitive practices began.

Apple stock closed Wednesday up 1.7% to $153.31, while Qualcomm shares closed up 1.18% to $56.61.