Absolutely not. Bitcoin will stabilize in the future if its market cap continues to increase and the market matures, sure. But it will never become a stablecoin.

A stablecoin has to be backed by something external, like the USD. Bitcoin is not backed by anything but its own value, which means that even if its value continues to stabilize in terms of USD, it will never truly be stable as it is not pegged to fiat currencies via a central pegging mechanism.

That's honestly one of the advantages of using bitcoin as a store of value as well, it's completely separate from the fiat system and even though there is short term volatility, in the long run it should hold its value due to its limited supply.