The Verdict: Need More Info
Your partner cannot sponsor you until they are a permanent resident themselves. If they are applying for it, ask whether you can be included in their application as their spouse or partner.
A pending application, an approval in principle or a work permit is not enough. The sponsor must hold permanent residence on the day the sponsorship is filed.
If your partner is applying through an economic route such as Express Entry or a provincial nominee program, you can usually be included in that application as an accompanying family member. That brings you both to permanent residence together, and is often faster than being sponsored afterwards. Adding someone late in the process is possible but has its own rules.
If their application is close to a decision, it may be simpler to wait for it and then apply for sponsorship. If they have not applied for permanent residence at all, that is the first step, and the skilled migration quiz covers the routes.