Halfords is the target of a £1.4bn merger, with vehicle company Redde Northgate eyeing a deal.
Both firms are thought to have been involved in detailed discussions about a collaboration before the offer was made.
According to a City source, Redde Northgate previously put forward a nil-premium merger before the plans were scrapped due to price disagreements.
Halfords is thought to believe that the deal undervalues the business, the Telegraph reported.
It is thought that Redde Northgate could now launch a new offer if the valuation gap between the two companies closes.
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A source close to the discussions told the newspaper: “There were discussions about what an integration of the two businesses might look like but there were questions over the valuations of both companies.
“Both share prices weren’t doing fantastically well at the time so there is nothing live at the moment. However, it could come back”.
The news follows Halfords making a rescue deal for online bike retailer Wiggle, which fell into administration late last month.
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