The trial is likely to shed light on alleged links between militant groups and the Pakistani secret intelligence service. Mr Rana denies the 12 charges that have been levelled against him.
His lawyers say he was tricked by Headley, a longtime friend from their days at a Pakistani military school. Mr Rana was arrested in 2009, and if convicted, he faces a life sentence.
"What this case is going to be about is David Headley's betrayal of his friend Rana, his betrayal of the US , his betrayal of all human and decent values," Mr Rana's lawyer Charlie Swift was quoted by the Associated Press as saying.
Mr Rana was merely "friends with a terrorist", he said.
Prosecutors say that in 2006 Mr Rana allowed Headley to open an office of his Chicago-based immigration services firm in Mumbai, which Headley then used as cover to scout sites for the 2008 attack.
In November 2008, a group of 10 gunmen the US says were trained by militant group Lashkar-e-Taiba attacked the Taj Mahal and Oberoi hotels, a Jewish centre and a major train station, each of which Headley had scouted in advance.
In March 2010, Headley, a US citizen who spent much of his childhood in Pakistan, pleaded guilty to taking photographs and video of the targets. He could face up to life in prison and a $3m (£1.86m) fine.
In addition, prosecutors say Headley and Mr Rana plotted an attack, which was never carried out, on Danish newspaper Jyllands-Posten.
Also charged with planning the Mumbai attack are four Pakistanis, including one said by prosecutors to be a Pakistani intelligence officer. None are in US custody.
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