Babcock International and VT Group are in talks about merging their companies into a support services powerhouse.
The companies said they had "agreed a basis for a mutual exchange of information" but no deal had been reached, they said.
The announcement came after VT said that it had dropped its bid approach for infrastructure firm Mouchel.
VT had rejected Babcock's earlier offer of talks, but faced increasing pressure from its shareholders to do a deal.
Evolution analyst Harry Philips said the move showed VT had responded to the mood among shareholders.
"This clearly is progress and is significant because it is a step forward and shows they have agreed some parameters," he said.
"It doesn't suggest it is a full opening of the books, but Babcock are clearly now going to have access to information that they wouldn't have had [before]," Mr Philips said.
"I think it's all about price now [between VT and Babcock]," Angela Lascelles, joint managing director at investment group OLIM, which holds 1.49% of VT shares.
Babcock's offer last month valued VT at about £1.3bn, or 715p a share. Many investors believe the company is worth up to 800p a share.
Babcock, which maintains the Royal Navy's submarines, had said any deal would be subject to VT withdrawing its approach for Mouchel.
VT sold its shipbuilding operations to BAE Systems last year, and had a strategy to move away from the defence sector.