French Open: Sunday 25 May to Sunday 8 June Coverage: BBC TV, BBCi, Radio 5 Live and the BBC Sport website.
Bogdanovic is currently ranked 243 in the world
Alex Bogdanovic and Katie O'Brien were beaten on Thursday to end British hopes in qualifying for the French Open.
Of the seven Britons trying to make the first round proper at Roland Garros, Bogdanovic and O'Brien were the only two to win their opening matches.
But Bogdanovic, Britain's number three man, then went down 0-6 6-4 6-1 to Spain's Miguel Angel Lopez Jaen.
And O'Brien, Britain's second-highest ranked woman, suffered a 6-4 6-2 defeat by Kristina Barrois of Germany.
Bogdanovic had beaten Mathieu Rodrigues of France 6-0 6-3 in the opening round of qualifying, while O'Brien had seen off fellow Briton Melanie South 7-5 6-1.
Anne Keothavong, Elena Baltacha, Naomi Cavaday and Josh Goodall all fell at the first hurdle.
British number one Andy Murray will learn the name of his first-round opponent when the French Open draw is made of Friday.
• Bogdanovic and Goodall have been given wildcards for the Artois Championships at Queen's Club, starting on 9 June. The two remaining wildcards went to Jonas Bjorkman and Xavier Malisse.