According to this brochure from SAAB:

GE Aviation will provide and sustain the fighter’s engines in Canada.

But that's from 2021, so maybe the current proposal is for a US made engine.

This from 2026 says:

The Gripen E is based on an American engine (F414). This means dependencies on licenses and authorizations. In a context of sovereignty, this is a point that needs to be addressed, not circumvented.

I wonder if a Canadian or European made engine is still possible. I guess anything is, at some a cost.

Investing in any aircraft with critical components controlled by Canada's greatest current threat seems a poor strategy.