The note from Chatterjee outlines three industries the firm thinks would be a good fit for Apple to make strategic acquisitions and names three companies Apple should buy: Netflix, Activision Blizzard and Sonos. This is speculation from Chatterjee but comes as Apple's long run of growth from the iPhone begins to dwindle. Chatterjee even notes specifically that the combination of Apple-Netflix is unlikely.
Apple and Netflix did immediately respond to requests for comment on J.P. Morgan's speculation.
"We believe Apple can drive synergies between its leading position in smartphones and the rapid transition of video consumption to mobile to drive stronger services growth," Chatterjee said. "We find Netflix as the best strategic fit, although we appreciate a combination is less likely as Netflix is unlikely to be a seller for a modest premium."
While Chatterjee said it would be difficult and pricey for Apple to acquire Netflix, he provided three reasons why the streaming service would be the best fit for Apple. First, Netflix fits with Apple's preference of being an "aggregator of content," he said, rather than a traditional media company like Sony Pictures. Second, the Netflix subscription model fits with Apple's services revenue model. And third, while difficult, Netflix would be easier to acquire than Hulu and Amazon Prime.
J.P. Morgan thinks Apple needs to buy instead of starting a streaming service on its own.
"Video streaming, including original video content, is a highly competitive market with established traditional media houses as well new entrants fighting aggressively for incremental subscribers, which is likely to make it difficult to scale any new platform to compete effectively," Chatterjee said.
Additionally, J.P. Morgan thinks a combination with Netflix could streamline Apple's advertising revenue.
"An acquisition of Netflix could help Apple drive consumers faster to their gateway app, which is serving as an aggregator of content and multiple subscriptions, and could enhance the opportunity around potential advertising revenues in the future," Chatterjee added.
Shares of Apple and Netflix rose 2.8 percent and 3.4 percent, respectively, in Monday trading.
Disclosure: Comcast, which owns CNBC parent NBCUniversal, is a co-owner of Hulu.
contributed to this report.