Kenney is meeting Friday with labour ministers in Toronto to discuss the controversial program. The Canada Job Grant will go into effect in April 2014.
Discussions that began early Friday morning are described as "frosty" and "tense" by one person privy to the meeting. The premiers are standing firm in their assertion that the program is not working in its current form.
In an interview with CBC New Network's Power & Politics on Thursday Kenney said the provinces won't get a "one size fits all" approach, which has been the main point of contention since Ottawa announced the program in the budget last March.
"We'll be having 13 agreements, with 13 provinces and territories. We're talking about a great deal of flexibility here," Kenney said.
The provinces have been asking the federal government to reconsider proposed changes to the way the provinces provide skills training to Canadians looking for work.
They're particularly unhappy about Kenney's plan to shave $300 million from the Labour Market Agreement that the federal government brought in six years ago.
The federal program provides funds to train unemployed workers who are not eligible for employment insurance, but the provinces say the proposed changes will put funding for key programs that are working well now at risk.
Those who will be impacted the most by the proposed changes, according to the provinces, are low-skill workers such as youth, Aboriginal Peoples, persons with disabilities, social assistance recipients, recent immigrants, older workers and long-term unemployed Canadians.
Job grants plan "not flexible enough"
Ontario Premier Kathleen Wynne said on Thursday that the Canada Job Grant will cost Ontario $232 million to continue delivering programs for low-skilled workers.
"The way that the Canada Job Grant is configured doesn't work; it's not flexible enough for the provinces," Wynne told reporters in Toronto.
Wynne, also chair of the Council of the Federation, which brings together Canada's premiers and territorial leaders, said the provinces need more flexibility to design and deliver the programs to those most in need.
Shirley Bond, the B.C. minister of jobs, tourism and skills training, told CBC News in an email Thursday "the proposed changes mean that the British Columbians who most need support to enter the job market will be left standing on the sidelines."
B.C. expects there will be one million job openings in the next decade and is concerned the proposed changes by the federal government will not support low skilled or underemployed individuals
The shift "away from essential skills training is unanimously opposed by Canadian premiers and labour market ministers," Bond said.
Kenney has often said the way the current system works turns most of the people involved are "habitual welfare recipients," adding that if the provinces want to train their welfare recipients, they should pay for it out of their own budgets.
The premiers and territorial leaders will gather for their annual fall meeting in Toronto on Nov. 15.