What is your reasoning on that?
First, several announcements by BAE previously have indicated cooperation at the subsystem level and on engines (
https://www.janes.com/defence-news/news-detail/japan-uk-discuss-partnership-on-fighter-jet-engines).
They have already signed an agreement with Lockheed Martin to assist with the design of the airframe and LO aspects.
Japan will want a sizable domestic industry input in regards to systems and of course airframe construction and assembly.
Two large and two small partners on Tempest might strain the workshare and make it impossible to reach agreement. Building F-35s across the world made some economic sense when talking of production runs of thousands, but 450-500 Tempests
We don't know what the official operational requirements are behind Tempest and F-X, they might not be compatible. On the face of it, both Tempest and F-X are likely to be very similar in design and the wider combat system is likely to be too but there might be important differences in role and how they are designed to meet whatever parameters have been laid down.
There may well be US technology issues that might hamper sharing of information between Japan and the UK and Italy/Sweden too.
We don't know much about the unmanned aspects of either Tempest or F-X, work has only just begun. There might be room for synergy but equally the US might offer the Boeing Loyal Wingman or XQ-58 to both nations or they might go it alone with Mosquito and whatever Japanese system emerges.
I've seen nothing so far that indicates Japan is likely to chuck away its work done so far (ATD-X etc) and jump onto Tempest. That discussions about the option of full partnership have taken place I don't doubt, but I don't see it happening unless US support vanished from F-X.