Further education is capable of providing the bite-sized courses, running for as little as two or three weeks, which firms say they need but, according to the Association of Colleges, this can only happen on a big scale if the funding rules are changed.
The point was pressed home at a reception staged in Westminster by the AoC which was attended by civil servants, colleges, businesses and politicians from the three main parties.
The occasion was intended to highlight the record of colleges - often accused of being too distant from business - in providing training for industry.
As part of its Colleges at the Heart of Business campaign, the association has been digging up the figures to prove it. AoC research shows colleges, while spending significantly less money on training than business itself, actually provide more - 200 million days a year compared with 60 million.
And a third of college income is from employers rather than the Learning and Skills Council. But colleges could do far more, it argues, if they were given more freedom.
David Gibson, chief executive of the AoC, said: "The further education sector wants to continue to be innovative and responsive when it comes to meeting industry's training needs. Colleges need to be given the freedom to compete against private trainers on a national level."
Achievement rates are rising among adults who take college courses, according to the Adult Learning Inspectorate. But, says Mr Gibson, bureaucratic barriers, as well as funding problems, have restricted FE's work in this area.
It may be that some employees need to be trained for specific tasks and that a college can offer training over two or three weeks which meets the company's needs.
The problem comes when that training, which might be as simple as introducing staff to a new piece of machinery, does not fit with the range of national vocational or other qualifications which are on offer. If the training is not government-recognised, it doesn't attract funding from the LSC.
Such obstacles are an increasing frustration for the AoC. The Government wants to see 3.6 million workers getting to level 2 (GCSE equivalent) by 2010.
Current funding, even if all of it were to reach colleges, gives them the space for 60,000 extra adults a year. Employer training pilots, which have started in six LSC areas, are being used, in part, to see whether public funds can be used effectively on short courses which are not related to qualifications.
The Government is moving towards giving employers and colleges more freedom to decide locally what type of training packages are needed. The Treasury, which is taking an increasingly high profile in the skills debate, is looking closely at whether funding could be loosened up.
Treasury minister John Healey, formerly in charge of adult skills at the Department for Education and Skills, was at the reception.
There is a feeling among colleges that the Treasury will breathe new life into FE and the warm words from Mr Healey, as he once agin finds himself on the FE circuit, are winning new friends for a department once seen as a dead hand.
Ed Balls, chief economic adviser to Gordon Brown, the Chancellor, says the employer training pilots will test whether government money can be entrusted to colleges and employers in this way.
He said: "We want to look at people's training needs up to level 2.
"But I don't think there should always be pressure for them to lead to an NVQ.
"We are trying to give local LSCs some flexibility and these things are being tried out."
Qualifications-based training must also be modified to make short courses easier to run, says Ivan Lewis, the adult skills minister.
"We are working to create a more unit-driven system," he said.
"It is important for companies to be able to give people bite-sized qualifications."
The AoC says the barriers are to do with the burden of red tape as well as funding rules.
The LSC's claim that its underspend during its first year, 20012, was partly caused by colleges failing to claim funds, drew an angry response from Mr Gibson.
He said the procedures for drawing down funding needed to be simpler.