The Future Circular electron-positron Collider (FCC-ee) is a proposal for a 91.17 km collider, which would operate in four modes with energies ranging from 45.6 GeV (Z-pole) to 182.5 GeV (ttbar-production). At high energies the beam lifetime could be as low as 6 minutes, requiring the beam to be continuously topped up to reach a high integrated luminosity. This top-up injection would use a separate booster ring in the same tunnel as the collider, which would accelerate the beams to the collider energy. The booster ring should achieve a lower equilibrium emittance than the collider, despite challenges such as a long damping time and no magnet-strength tapering to compensate for the impact of synchrotron radiation. For top-up injection into the collider, we consider two strategies: conventional bump injection, employing a closed orbit bump, and injection using a multipole kicker magnet. On-axis and off-axis sub-schemes will be studied for both. We compare these injection strategies on aspects including spatial constraints, machine protection, perturbation to the stored beam and hardware parameters.