"About a thousand a year- that is pretty significant," he told reporters at NATO headquarters in Mons in southern Belgium.
Jones declined to say how many NATO instructors would be sent to Iraq or what kind of force would be deployed to protect them, saying it "depended on the willingness of member states".
Senior officers suggested the number could be between 350 and 3,000, though the higher figure was judged very unlikely.
"I think it would need not exceed 3,000,"Jones said. "I'm confident it will be less than that."
The NATO contingent will work on three fronts -- developing a military academy on the outskirts of Baghdad, channelling supplies of military equipment donated by alliance members and advising officers in the new Iraqi army.
Jones submitted earlier this week an "operation plan" to put into effect the training mission. This is being considered by NATO's military committee before being passed to ambassadors from the 26 NATO member states for approval later this year.
At present fewer than 70 NATO personnel are in Baghdad where they have already begun training military headquarters staff.
"Now we are working out of the Green Zone ((a fortress-like compound in the centre of Baghad that also houses the US and British embassies among other official buildings) but we are looking at alternatives to base trainers outside," a senior NATO spokesman in Baghdad told AFP Wednesday.
Jones said he could not say whether the military academy would be functioning by January, the date set for general elections in Iraq.
"Sixteen or 17 nations out of the 26 have indicated a willingness for duty inside Iraq," he said.
Others, in particular France and Germany, have said they will contribute to the programme but not on Iraqi soil.
About 20 Iraqi officers are expected in the Norwegian town of Stavanger next week for a week's training in a NATO facility.