The 31-year-old Bristol man is accused of hiring a hit man to kill his Swedish bride, Anni, 28, in Cape Town in November, The Guardian reported Tuesday.
Anni Dewani was found dead of a bullet wound in the back of an abandoned cab.
The cab driver and Shrien Dewani told police they had been hijacked.
Lawyers for Dewani, who suffers from post-traumatic stress disorder and clinical depression, told a hearing at Woolrich crown court they will question whether their client can receive a fair trial if extradited.
They also plan to bring up prison conditions in South Africa and whether Dewani's mental state would allow him to participate meaningfully in legal proceedings.
Lawyer Julian Knowles indicated it was uncertain whether his client would recover in time for extradition proceedings.
The full extradition hearing won't be held until May.
Notable deaths of 2014 [PHOTOS]