My dogs have to have a good recall and must not chase the deer (illegal) we have a good chance to see when hiking. With my super high prey drive Doberman, he had lessons at home when he was young. I used enticing faux prey to train him. He had to come first, then he could chase the prey. We advanced gradually to other animals.
You need a helper and a bucket, an animal pelt or stuffie with smelly animal scent and a string. Dog is enticed, recall, if dog doesn't come, bucket is put over wiggly "prey." Chasing without coming gets him nothing. Repeat. When dog comes first (with help of a long line, if needed) dog is released to get pelt on a string...gets to chase, have fun. Recall first, then the chase is on.
I then practiced with squirrels. With squirrels, I didn't care if he chased them..they never get them. With deer, dog must come and doesn't get to chase as a reward. (by this time we're on a variable reinforcement schedule and the squirrel chasing happens enough to satisfy the need) But as far as ignoring....no, I don't expect a dog to ignore a squirrel, just to come when called. It's who they are....predators. Can't really take that out of them. But they can learn that they don't have to have direct access to the squirrel in order to get to chase the squirrel...by not chasing the squirrel and coming to me first, they get the squirrel, or the chance to chase. Only Lyric was good at that. The Chi's I didn't do all that with but I don't have trouble with them anyhow. And even Lyric wasn't perfect. He might begin to chase some deer, but then did come when called after starting out after them. Once, it took two tries to call him off. It's definitely not an easy instinct to fight against.
As far as squirrels, it's highly doubtful that your dog will catch one and it's an awful lot of fun and good exercise and a good outlet. (so necessary to have an outlet for that drive)