An MP has joined those questioning if a 112 mile-long (180km) power line should be suspended mostly on new pylons.
National Grid plans to install a high voltage line, between Norfolk, Suffolk and Essex, to carry electricity from offshore wind turbines.
Richard Bacon, Conservative MP for South Norfolk, said he was concerned the approach taken by the company "precluded certain options".
The publicly listed firm is currently consulting the public on the project.
It would use 164ft high (50m) steel pylons, except for where it would run underground through the Dedham Vale area of outstanding natural beauty on the Suffolk/Essex border.
National Grid said the "essential" line would also be used by the proposed new Sizewell C nuclear power station.
But the scheme has come up against opposition from people across the region, who argue the pylons will be unsightly and damaging for wildlife.
More than 7,000 of them have signed a petition calling for the line to run offshore.
Mr Bacon said: "I think there's a general view that the approach that National Grid has taken has precluded certain options from the get-go, and then tried to consult on a narrow range, rather than looking at it properly.
"I have a particular concern about why they wouldn't bury them underground.
"But that's aside from the other question of whether we shouldn't have an offshore grid, which I've always thought we should.
"That might then make it much more logical to have a sub-sea route entirely around to Essex."
Earlier this month, the Essex MP Bernard Jenkin said the plan was a "non-starter".
National Grid company director of new infrastructure, Zac Richardson, has said the firm did not believe it was "technically feasible or economic" for the line to go offshore.