The decision is expected to be finalised before the group's full-year results on Wednesday which will show that profits at B&Q slumped 30 per cent last year from pounds 83m to pounds 55m.
Sir Geoff Mulcahy, chief executive, has become alarmed at the poor performance at B&Q, once the driving force of Kingfisher's growth but now its chief problem area.
His view is that Mr Hodkinson and his management team have spent too much time opening new stores and not enough on getting the existing stores right.
The expansion of the huge Warehouse store format will be reined back. This will please analysts who have been concerned that the huge superstores were grabbing sales from the standard-size B&Qs.
Sir Geoff has been spending an increasing amount of time at the B&Q head office trying to sort out the problems. He has been critical of poor planning of staffing levels, poor product layout and high levels of shopper shrinkage, or theft.
Mr Hodkinson, 52, was on a two-year contract and will therefore be in line for compensation of up to pounds 600,000. He also holds share options worth almost pounds 200,000.
Already a multi-millionaire from his early days at B&Q, Mr Hodkinson has been with the company since 1972, though he left in 1994 to spend a year in the US at Home Depot, the DIY giant.
It is thought that Sir Geoff has decided Mr Hodkinson's entrepreneurial skills are better suited to an expansionary strategy rather than the cost- conscious approach now necessary.
The most likely internal candidate to succeed Mr Hodkinson is his deputy, Martin Toogood, though an external candidate is possible.
Mr Hodkinson will be the fifth director to leave the Kingfisher board since it announced a profits warning last January. A year ago the company axed four directors including then chief executive Alan Smith and finance director James Kerr Muir with compensation payments totalling pounds 2.75m.
Sir Nigel Mobbs has also retired as chairman and has been replaced by Sir John Banham, former director general of the CBI.
City analysts expect Kingfisher to announce a small decline in its group profits to around pounds 275m on Wednesday, although Woolworths is expected to have performed strongly.