A Muslim can offer Prayers inside the Ka`bah. The Prophet (peace and blessings be upon him) entered the Ka`bah and performed Prayer there, and so did some of the Prophet’s great Companions (may Allah be pleased with them).

In this regard, we cite what Sheikh Sayyed Sabiq states in his well-known book, Fiqh Us-Sunnah: Offering Prayer in the Ka`bah is valid regardless of whether it is an obligatory Prayer or a supererogatory Prayer. Ibn `Umar reports: The Messenger of Allah entered the house [the Ka`bah] with Usamah ibn Zayd, Bilal, and `Uthman ibn Talhah and they closed the door behind themselves. When they opened the door, I was the first to come upon them and I asked Bilal, “Did the Messenger of Allah pray [while he was inside]?” He said, “Yes, between the two Yemeni pillars” (Al-Bukhari, Muslim, and Ahmad).

Sheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, states:

It is proven that the Prophet (peace and blessings be upon him) entered the Ka`bah and performed Prayer there, and so did some of the Prophet’s great Companions (may Allah be pleased with them). There are many hadiths reported in this concern in Al-Bukhari and Muslim. Also, An-Nawawi stated in his book Al-Idah: “It is recommendable for one to enter the Ka`bah bare-footed and offer Prayer therein. It is better to pursue the spot where the Prophet (peace and blessings be upon him) used to perform Prayer. On entering the Ka`bah, the Prophet (peace and blessings be upon him) used to walk from his entrance until there were about three cubits between him and the opposite wall and perform Prayer, as recorded in Al-Bukhari. This can be done on condition that no harm is inflicted on the person or on others. If there is any such harm, one should not enter the Ka`bah.”
As for the reward for entering the Ka`bah, there are many hadiths. Some of them can be traced back to the Prophet (peace and blessings be upon him), while others have their chain of transmission cut before it reaches up to the Prophet (peace and blessings be upon him). Among these hadiths is one that reads: “Whoever enters the Ka`bah and performs Prayer therein acquires a reward and one of his sins is expiated.”