BAE Systems is reported to have put in a solo bid for the Devonport naval dockyard in Plymouth.
The Financial Times says that BAE and the US private equity group Carlyle have put in separate offers.
The Ministry of Defence (MoD) is understood to have been keen for the two to make a joint offer.
BAE already owns the UK's only submarine-building facility in Cumbria, and Devonport refuels and refits all of the Navy's nuclear submarines.
The MoD is believed to be concerned about becoming too reliant on BAE as the £15-20bn programme to replace Trident is undertaken.
The FT reported that people close to the talks said the situation was still fluid and that talks about a joint bid were continuing.
Other companies rumoured to be considering bids include the US defence firm General Dynamics.
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