There will be a particular focus on how Brown funded the military, which lost 179 soldiers in the Iraq campaign and is currently engaged in fierce fighting in Afghanistan.
In his testimony to the inquiry in January, Geoff Hoon, the defence secretary at the time of the war, said his ministry had lacked funds for years before invasion.
Friday's edition of The Times, a British newspaper, carried comments from General Charles Ronald Llewelyn Guthrie, who led the armed forces from 1997 to 2001.
He said: "Not fully funding the army in the way they had asked ... undoubtedly cost the lives of soldiers.
"He [Brown] should be asked why he was so unsympathetic towards defence and so sympathetic to other departments."
Jocelyn Cockburn, a lawyer for relatives of soldiers killed in lightly armoured Snatch Land Rovers in Iraq, said that she was urging Chilcot to challenge Brown over funding concerns.
"Specifically, was he aware of concerns around the lack of armoured vehicles and did he receive any requests for funding [particularly in the period 1997-2006] to purchase armoured vehicles?" she wrote in a letter to Chilcot.
The use of the Snatch trucks has been the focus of growing anger here after a number of soldiers were killed by roadside blasts in the vehicles in both Iraq and Afghanistan.
Chilcot said he would not call Brown and other serving ministers until after the election to avoid the hearing "being used as a platform for political advantage".
However, following pressure from political rivals, Brown offered to appear beforehand.
After two years trailing far behind the opposition Conservatives in opinion polls, Brown's governing Labour Party has experienced a recent boost in support.
Any fresh revelations linking him to the still-divisive Iraq conflict, seen by many as a black mark on Labour's 13 years in power, could be highly damaging.
Brown was finance minister from 1997 until 2007, when he took over from Tony Blair as prime minister.
Blair appeared before the same inquiry in January.