I'm not a native English speaker, but I'd like to be able to speak like one.
I can't speak English like a native English speaker, but I'd like my pronunciation to be like theirs.
この場合、次のような言い方ができます。
ーI'm not a native English speaker, but I'd like to be able to speak like one.
「私はネイティブではないが、ネイティブのように話せるようになりたい」
ーI can't speak English like a native English speaker, but I'd like my pronunciation to be like theirs.
「私はネイティブのように英語が話せないが、発音がネイティブのようになって欲しい」
pronunciation で「発音」
ご参考まで!