Praise be to Allah.
It is not permissible to sell gold for gold or silver, or whatever comes under the same category such as paper money, unless the exchange takes place on the spot.
That is because of the report narrated by Muslim (1587) from ‘Ubaadah ibn as-Saamit (may Allah be pleased with him), who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Gold for gold, silver for silver, … like for like, same for same, hand to hand. But if these commodities differ, then sell as you like, as long as it is hand to hand.”
Paper money comes under the same ruling as gold and silver.
The Permanent Committee for Ifta’ was asked: If one man sells a piece of gold jewellery to another, but the purchaser does not have some or all of the price with him, or not after a few days or a month or two months, is this permissible or not?
They replied: If the price for which he is buying the gold jewellery is to be paid in gold or silver or what comes under the same heading of paper money or cheques, that is not permissible; rather it is haraam, because of what it involves of riba an-nas’iah. But if he is purchasing it in return for other goods, such as fabric or food and the like, then the delay in payment is permissible. "Fataawa al-Lajnah ad-Daa’imah (13/466)"
The Committee was also asked:
There is an agent who sells gold to all the shops on credit for a known price, whether that is for cash or on credit. We all buy from him on the basis that every week we will make a payment until it is all paid off, and that may take more than two months. Please note that the price of gold is not stable internationally.
Selling gold for silver or what takes its place of modern currencies is not permissible unless the exchange takes place on the spot. "Fataawa al-Lajnah ad-Daa’imah (13/471)"
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
It is not permissible to give gold to the purchaser and not receive the payment until after a while, because this is riba. "Fataawa Noor ‘ala ad-Darb, by al-‘Uthaymeen.."
See also the answer to question no. 22869 .
And Allah knows best.