Praise be to Allah.
We have discussed previously the muraabahah transaction in which an item is sold to the one who asked for it to be purchased, noting that there are two conditions for it to be permissible:
1. The bank or company should take possession of the house in a legal sense before selling it to the one who wants it and asked for it.
2. The party that purchased the house should take possession of it [meaning that the previous occupants should have vacated the property] before selling it to the customer who wants to buy it.
It is not stipulated that the party with whom the muraabahah transaction in which an item is sold to the one who asked for it to be purchased is done should be an Islamic bank. So long as the conditions mentioned above are met, even if the seller of the item is a non-Muslim investor, there is nothing wrong with dealing with him, because it is permissible to deal with the disbelievers, buying and selling, and this is not regarded as taking them as friends and allies in the sense that is not allowed, and it does not mean that you are getting involved with their other corrupt dealings, or consuming their unlawful wealth, so long as the transaction that the Muslim is doing with them is itself permissible.
Al-Bukhaari said in his Saheeh:
Chapter on buying and selling with the polytheists and those who are in a state of war with the Muslims.
In this chapter, he quoted the hadith of ‘Abd ar-Rahmaan ibn Abi Bakr (may Allah be pleased with him), who said: We were with the Prophet (blessings and peace of Allah be upon him) when there came a tall polytheist man with his hair in disarray, driving some sheep. The Prophet (blessings and peace of Allah be upon him) said: “Do you want to sell or give for free?” The man said: Rather I want to sell. So he bought a sheep from him. Al-Bukhaari (2216).
It was narrated from ‘Aa’ishah (may Allah be pleased with her) that the Prophet (blessings and peace of Allah be upon him) bought some food from a Jew to be paid for at a later date, and he gave him an iron shield as collateral (rahn). Narrated by al-Bukhaari (2509) and Muslim (1603).
Ibn Daqeeq al-‘Eid said regarding what we learn from the hadith of ‘Aa’ishah:
This indicates that it is permissible to deal with the disbelievers, and no attention is to be paid to their (other) corrupt dealings." (Ihkaam al-Ahkaam 2/145).
Ibn Battaal said: Dealing with the disbelievers is permissible, except for selling that which those who are at war with the Muslims could use against them." (Fath al-Baari by Ibn Hajar 4/410).
Conclusion: there is nothing wrong with doing this muraabahah transaction in which an item is sold to the one who asked for it to be purchased with a non-Muslim, if he meets the conditions required to make that transaction permissible.
And Allah knows best.