It is not permissible to keep and train foxes, wolves and other predators such as lions and tigers, because there is no benefit in that, and because keeping them may lead to great harm, as there is no guarantee that they will not get loose and harm people. Moreover, keeping them is a waste of money and spending on something inappropriate. It is also an imitation of those spendthrifts who have no ambition except satisfying their whims and desires. 

Al-Nawawi (may Allah have mercy on him) said in al-Majmoo‘ (9/286-287): The second category of animals is those in which there is no benefit, so it is not permissible to sell them, such as dung beetles, scorpions and snakes. … Our companions said: that also includes wild animals that are not suitable for hunting with or fighting, and cannot be eaten, such as lions, wolves, tigers, bears and so on. Sales of such animals are not valid, because there is no benefit in them. End quote. 

Zakariya al-Ansaari (may Allah have mercy on him) said: 

Sales of insects that are of no benefit are not permissible, and neither are sales of wild animals that are of no benefit, such as lions, wolves and tigers. The awe involved when kings keep such animals and show that they can handle them is not regarded as being of any benefit, unlike cases in which there is some benefit, such leopards for hunting or, it was said, elephants for war. End quote. 

Fath al-Wahhaab, 1/273 

The Scholars of the Standing Committee for Issuing Fatwas were asked about the shar‘i ruling on dealing in or keeping animals that are used to fulfil whims and desires, including predators such as wolves, lions, foxes and so on.

 They replied: 

It is not permissible to sell predators such as wolves, lions, foxes and other wild animals that have fangs, because the Prophet (blessings and peace of Allah be upon him) forbade that. And because it is a waste of money, and the Prophet (blessings and peace of Allah be upon him) forbade wasting money. End quote. 

Fataawa al-Lajnah al-Daa’imah, 13/38-21 

It is well known that many of those who keep and train predators find that the animal does not forget its wild origins and devours its keeper, or attacks him or someone else. 

There is a story that a Bedouin took a young wolf and raised it on the milk of a sheep he had, and he said to himself: If I raise it with the sheep, it will develop compassion towards it and will protect it, and it will be better than a dog, and will not know the ways of its own kind. But when it grew strong, it pounced on the sheep and devoured it, and the Bedouin said:

You ate my little sheep although you grew up amongst us;

How did you know your father was a wolf?  

Muhaadaraat al-Udaba’, 1/115 

For more information please see the answer to question no. 103706 

And Allah knows best.