Alan Revie, chairman and chief executive of the Glasgow-based company, is a majority shareholder in the company. Industry analysts have speculated that Revie could receive up to £50m if a sale went through.
The DT listed Nationwide Autos, Micheldever Tyres and Kwik-Fit as potential bidders.
Revie told the Glasgow Herald: “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."