LU had ruled out a request from EH to build the line on top of the arches, as it believed the structure was not strong enough. However, it has now agreed to review the possibility of drilling through the arches so that steel poles could be put in place to support the line.
Alan Thornton, project manager for the East London Line, said LU designers will examine the proposal this month.
He said: "EH has asked us if it is possible to build a lightweight structure and drill through the arches to support the line. It's almost like building a bridge."
Thornton added that an initial examination suggested that the proposal would not work because the arches would probably impede lifts and escalators.
The review is the latest twist in a project beset by controversy.
In January, EH insisted that the Braithwaite Viaduct, one of the oldest of its kind, be listed because it feared that it would be demolished as part of LU's plans.
At first, LU believed that the listing would delay construction by up to 18 months and that it would mean the adjoining arches could not be demolished. But legal advice has since suggested that this is not the case.