DUP Foyle MLA Gary Middleton
Gary Middleton, who represents Foyle, said he did not know which office was involved.
It emerged on Wednesday that three Sinn Féin offices received £10,000 payments from the fund, which have since been repaid.
Two of those are former mayors of Derry, including Senator Elisha McCallion.
MP and MLA constituency offices are ineligible for the scheme.
The DUP, SDLP, Ulster Unionist Party and Alliance have all said that none of their MPs or MLAs received money from the Small Businesses Grant Support Scheme.
Mr Middleton told the BBC’s Good Morning Ulster on Thursday: “I can be very clear in terms of DUP MLAs, MPs, representatives, that no payments were made to those elected reps.
“I am led to believe that there was one case of a landlord having received the payment.
“That landlord should repay that money if that is the case.”
Mr Middleton said he was not aware if the money had been repaid.
Payments from the fund were sent out automatically to 7,000 bank accounts, but it has emerged that some of the accounts which received the money were ineligible.
Sinn Féin said its offices did not qualify nor did it apply for the scheme.
The party said the funds received by three of its offices had been returned to Land and Property Services, which administered the grant.
Figures released by the Department for the Economy (DfE) show that 24,700 payments were processed under the Small Businesses Grant Support Scheme.
There were 452 payments, totalling more than £4.5m, which were made to those who may not have been eligible.
Mr Middleton said the assembly standards commissioner should investigate the Sinn Féin payments, adding the party faced “serious questions” about when the funds were returned.
On the payment to a DUP office landlord, he said: “Any case at all where payments have been made, albeit automatic, people should be open and honest about that and return it where appropriate.
“If a landlord of any representative received the payment for that property they should return it.”
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