According to Ouest-France, the French company has been given a mandate to part-purchase the business, which was put on sale by its Australian owners, Macquarie Group, last year.
The newspaper claims that Brittany Ferries is currently putting together an offer but is also seeking co-investors to complete the sale.
However, Macquarie Group, Condor Ferries and Brittany Ferries have all declined to comment.
Ouest-France have reported that Brittany Ferries are hoping to push ahead with the deal to counter an aggressive expansion plan from one of its competitors, Danish-owned DFDS.
It has also been reported that the takeover could secure vital ports – Saint-Malo, Poole and Portsmouth – from their competitors.
And Le Telegramme has reported that in an internal letter sent to Brittany Ferries staff, the company is hoping to prevent one of its competitors from buying Condor. It added that it was particularly concerned one of its rivals might wish to launch a Portsmouth, Poole or St Malo service.
Meanwhile, in St Malo on Saturday, police closed the approach road to the harbour after ‘gilets jaunes’ protesters began a peaceful three-hour sit-down protest just after 8am.
Those due to travel to Jersey narrowly avoided the disruption, with the first ferry of the day departing from the Breton port just minutes after the beginning of the demonstration.
However, those due to board Brittany Ferries’ service to Portsmouth were not so lucky. Photographs which appeared in the Ouest-France newspaper showed long tailbacks through the city and police were forced to close the approach road into the port.
The demonstrators began their action in October last year, initially protesting against nationwide environmental levies which caused fuel prices to rocket.
However, they are now rallying against the increase in the general cost of living in the country.
