U.S President Barack Obama has already authorised the deployment of over 3,000 troops to the country and the top U.S commander guiding the coalition effort said earlier this week that allies would send about 1,500 additional troops.
Fallon said troops in the "very low hundreds" would be sent next month.
He said that following air strikes by U.S.-led forces including Britain, Islamic State had changed its methods, moving away from use of large formations in open space.
"They are increasingly tucked away in towns and villages. That means they have got to be rooted out by ground troops.
"This has to be done by an own-grown army, not by western groups."
On Saturday, Islamic State fighters killed at least 19 policemen in a town in Western Iraq, as the group continues to seize territory in the region, despite aerial strikes.
Fallon told the newspaper that the exact number of Britons to be sent had not been finalised but that one of four teams would provide training in a Kurdish area and the remaining three in locations nearer to Baghdad.
"A key skill we are going to be helping with is counter-IED (improvised explosive devices), particularly vehicle explosive devices which the Iraqi army hasn't come across for some time," Fallon was quoted as saying.
