Reference: Fataawa al-Lajnah ad-Daa.imah lil-Buhooth al-‘Ilmiyyah wal-Iftaa. – Volume 11, Page 46, Fatwa No.5545
Question: A Muslim wanted to perform the obligatory Hajj whilst having an [outstanding] loan, so if he were to seek permission from the loaners and they permitted him to perform the Hajj, would his Hajj be acceptable?
Response: If the situation is as you have mentioned, with the permission of the loaners to perform Hajj before completing payment [of the loan], then there is no harm in performing the Hajj before completing the payment [of the loan]. And there is no affect [upon the Hajj] for being a borrower from them in such a situation.
And with Allaah lies all the success, and may Allaah send prayers and salutations upon our Prophet Muhammad (sal-Allaahu ‘alayhi wa sallam) and his family and his companions.