The Daily Telegraph said the firm – the largest independent fast-fit firm in the UK – is in talks with a number of parties about a possible takeover. It has reportedly hired PricewaterhouseCoopers to advise on a strategic review.
Repair company Nationwide Autos and its owner Phoenix Equity Partners have already made an approach to buy the company.
Other bidders are thought to include Micheldever Tyres and Kwik-Fit.
Several property-focused private investors are also thought to have shown an interest as many of National Tyres’ 200 branches are freehold-owned properties.
Alan Revie, chairman and chief executive of National Tyres, said: “It is no secret that National Tyres is a hugely successful business with ambitions to grow organically and by acquisition.
“It is inevitable that the turnaround we have brought about in its fortunes over the last five years will attract attention from all sorts of areas.
“However, we will not allow rumour and speculation to distract us from our primary goal of building a successful business that provides great service to its customers.”