Sure you can, what an issue to think about. Quite simple, you definitely can befriend even a wild cat. The most important thing is that you need to befriend them. This is essential.
You need to see the difference between a stray cat and a feral cat. They are quite different. The stray cat is a cat whom someone used to keep previously, like a former cat that has not got a home anymore; while a feral cat is totally wild, born in the wild nature. This type of cats varies from humans and cannot be adoptable as generally it is not adapted to people, its habitat is wild nature and not a cozy closed home, closed space. While stray cats can be befriended with some effort, feral cats will not get used to your presence.
Anyway do not forget that these are wild cats, so you need to take cautious measures to be on the safe side. Keep in mind that wild cats can never be domesticated and they are unpredictable so if you are firm in your decision of keeping a wild cat at home you will need to be aware of safety precautions just to make sure the cat will not attack you. Generally, cat bites are infected, some can be really serious, thus, to be on the safe side you better wear a long sleeved sweater and pants when you are in the process of befriending the new wild cat. One emergency signal that befriending will not work is when you notice that the cat starts to hiss or growl, looks sick can have a runny nose or eyes, scabs, sneezes sometimes or coughs, breathes heavily, this is not a good sign, you better stay away from the cat as it may be aggressive and can attack you.at your own house. When you face such a situation you should not lose a moment but simply call animal control agency. When you start the befriending part, you need to be patient and do it carefully. You need to make sure you will not intimidate the cat. So better approach the cat slowly, to get used to each other. If you are in a sitting or lying position this will make the process more smoothly.
The cat will feel safe in your company. If you give her something to eat this will only ease the situation and be beneficial for you. Take a smelly food, specific wet cat food or a tin of fish and put it in front of the cat for a moment to attract it and bring it closer to you. After this trick you will be associated with a positive thing in the cat’s brain as you are the person who fed her and every time she sees you can be sure that you are in her friends’ list. Then you can gradually start putting the yummy bite closer to you, as close as possible so that she comes to you without noticing or getting afraid. After some time, a week let’s say, you can come a little closer to the place where your cutie is eating. Do not make drastic moves, do not speak loudly not to distract the cat, simply stand quietly. Yeah and do not stare at the cat as well. Be a small part of the background and not that different from the other objects in the room. Let your cat sniff your hand, this will also help her to get attached to you.
Always remember that these cats were born into the nature and have never been kept inside as pets. Thus, the process of domestication and adaption may last longer, but is not impossible. You need to have patience and persistence and very soon you will get the first crops of your hard work. After extended period of time you will finally get the cat’s long awaited trust. She will start to come closer to you, you will be her comfort zone and you will become good and devoted friends very soon. You will discover hoy loyal and attached a cat can be, even more than dogs or any other pet. Just be patient enough to go smoothly through the adaptation process.