South Scotland MSP Joan McAlpine has written to the organisation asking them to make money available for an underground line, in light of regional opposition to planned pylons.
She pointed out that similar schemes have already been done for National Parks in England and Wales.
And she has asked Ofgem to meet constituents affected by the proposed line and hear about an alternative proposal incorporating a combined sub-sea and underground system put together by protest group Dumgal Against Pylons.
She said: “At the very least they should be given the opportunity to present their alternative plan, which for consideration by the regulator.”