They are also examining Tommy Main’s medical history amid reports he had mental health issues.
Mrs Cox, who won election last year to the Batley and Spen seat where she was born and raised, was shot and stabbed after holding a constituency advice surgery on Thursday.
Parliament will be recalled on Monday to let MPs pay tribute the popular and respected politician.
The announcement came as David Cameron and Jeremy Corbyn spoke of one of Parliament’s “most passionate and brilliant campaigners” on an emotional visit to the site where Mrs Cox died, in the town of Birstall, near Leeds.
Campaigning in the EU referendum remains suspended amid growing calls for the tragedy to put a halt to increasingly vitriolic political debate.
The Prime Minister issued a plea to drive intolerance “out of our politics and out of our public life”.
Labour leader Mr Corbyn said he had asked for Parliament to be recalled to enable politicians to pay tribute to Mrs Cox “on behalf of everybody in this country who values democracy … free from the kind of brutality that Jo suffered.”
Flags were flown at half-mast at the Scottish Parliament, the Palace of Holyroodhouse, and at government buildings across Scotland and the UK yesterday as a mark of respect. Hundreds of people attended a vigil in Parliament Square in London last night, with public gatherings in memory of Mrs Cox, a mother of two, held in Edinburgh and Glasgow.
A motion of condolence was lodged at Holyrood by Scottish Labour leader Kezia Dugdale, calling on all political campaigners to “conduct our public debate with good humour, understanding and her enduring spirit to make the world a better place”.
It has emerged that parliamentary security authorities issued guidance to MPs in the wake of Mrs Cox’s death, urging them to consider ending open-door constituency advice surgeries,