Reckitt said it was considering "all options" for the unit, which includes French's mustard and sauce products.
The Sunday Times reported that the company was mulling a sale to help fund its takeover of US baby food maker, Mead Johnson, for $16.6bn (£13.2bn).
Reckitt products include Cillit Bang cleaning goods and painkiller Nurofen.
Reckitt said French's Food was a "truly fantastic business with great brands", but was non-core.
"We have therefore decided to initiate a strategic review of food where we will explore all options."
Shares in Reckitt rose 11p to £72.97 in morning trading and are up 9% over the past 12 months.
The food division, which had sales worth more than £400m last year, could be worth about £2.4bn.
On Friday, Reckitt said it would cut the pay of chief executive Rakesh Kapoor to £14.6m from £25.5m in 2015.
Earlier this year, some shareholders had suggested that Mr Kapoor had pursued the Mead Johnson tie-up to ensure he hit lucrative bonus targets.
Mr Kapoor said the deal was in line with company strategy and would generate £200m of cost savings after three years - although it would not generate a return for about five years.
Consumer goods giant Reckitt Benckiser has confirmed it is beginning a strategic review of its food business, which could lead to it being sold off.