No, we don't have his Bird rights.
We have what's called his "Non-Bird" rights, which means we can give him up to a 20% pay bump next season, with 8% each season after for up to a five year contract. If he signed a non-Bird deal, it wouldn't count against the MLE.
However, it's unlikely he would do so. He can get more on a 3-year MLE deal than he can on a 4-year Non-Bird deal.