Your alien needs to be able to invoke a gas flow (easiest: breath out)
Speech sounds propagate through air. If you want to make yourself audible, breathing out air is part of that, in Earth's atmosphere, resonances and friction sounds will propagate and reach the listener. The alien should understand that basic concept, else it won't be able to learn speech by mimicing it. Once it grasps the idea, mimicing vowels will be no problem, as long as the alien has some cavities it can resonate while breathing out.
Some consonants will be a challenge, though,
The teeth may spoil some consonants
Unless the alien has giant and flexible lips over its "hyper" carnivore teeth, any "v", "w", or "m" or "p" or "b" subtleties would get lost, teeth are in the way, adding a slushing sound to everything, the alien has no lips, or its lips cannot be closed. Nasals sounds could be feasible, depending on the shape of the head and nose. Without a nose, the alien just needs some smaller, second cavity to mimic "n" or "ng".
Tongue and soft tissue
Shape may be no hurdle at all. The alien could mimic sounds using different parts of the mouth we do, its physiology would be different, sound similar. A flexible tongue would come in handy to do these tricks !
For realizing "g" and "z" and the difference between them, the alien must have certain soft tissue in the mouth. Without soft tissue, I doubt if the alien can produce credible voiced consonants, like "l" and "j". Also, plosives "d", "t" and "k" depend on softness differences, without soft tissue, it would be difficult to produce them, or they all sound like "k".
Hopeless ? No..
It does not have to be perfect
We can understand Donald Duck. Or a parrot. Humans are perfectly capable of interpreting speech, also when the speaker is impaired in some way. As long as the error made is consistent, the brain can recover skipped sounds, disambiguate similar sounds, or cope with a different vowel.. even wrong syllable timing can be comprehensible.. after a few minutes, a human listener can get used to that and regard the errors as "alien accent".