All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If the debt must be settled immediately and the debtor cannot afford the expenses of Hajj after settling the debt, then settling the debt takes precedence over making Hajj, even if it is the obligatory Hajj. Allaah The Almighty Says (what means): {And [due] to Allaah from the people is a pilgrimage to the House - for whoever is able to find thereto a way.} [Quran 3:97] The debtor is financially unable to go for Hajj.
If the creditor permitted the debtor to go for Hajj or if he can settle the debt at leisure, then it is permissible for him to perform Hajj. The Fataawa of the Permanent Committee state, “If the situation is as described, and the person or people who loaned you the money give you permission to go for Hajj before you pay off the debt, then there is nothing wrong with your performing Hajj before you pay off the debt, and the fact that you are in debt does not affect the validity of your Hajj in this case”.
Also, we see that helping your wife after delivery is not an excuse to delay performing Hajj, unless it is necessary to stay to look after her. In this case, you have a concession to delay Hajj for this excuse.
The majority of scholars said that Hajj must be performed as soon as possible, contrary to Ash-Shaafi‘i . As such, the man whose wife will give birth one week before Hajj can hire a maid to look after her during this period.