Executives at the company, sold last year to CVC Capital Partners, recently met with a number of pan-European contract hire and leasing companies to discuss opportunities.
These include ALD Automotive, Arval PHH, GE Capital Fleet Services, GMAC, Hertz Lease, HSBC, ING Car Lease and LeasePlan.
Kwik-Fit Fleet said that historically fleets and company car drivers in Europe preferred to use dealers ahead of fast-fit companies for the repair and replacement of tyres, exhausts, batteries and brakes.
It said its businesses in France, Germany and Holland all reported year-on-year growth with some centres more than doubling their business.
A spokesman said: 'Business is growing from pan-European fleets with whom we already have a relationship but also from fleets at a local level opting to use our outlets because of the quality of service and products we provide.
'By working with contract hire and leasing companies on a European basis we can leverage our business much more and dramatically increase our market shares in each of the three countries we have targeted.'