Pifco chairman Michael Webber said he had written to Kenwood on 5 July with an offer which named a price, understood to have been above the 212p market price at the time.
"We made a formal offer, which included a price, in a letter to every member of the Kenwood board," Mr Webber said.
At 215.5p Kenwood is currently valued at pounds 99m, against Pifco's pounds 48m. Kenwood has been under siege from UK Active Value, the fund run by corporate raiders Julian Treger and Bryan Myerson, who have called an extraordinary general meeting for a week on Monday to try and force the group to put itself up for sale.
They returned to the attack last week, after the food mixers group announced interim pre-tax profits more than halved to pounds 3.3m.
Pifco, which takes in the Salton and Russell Hobbs brands, disclosed its interest last week. It wants to put Britain's two independent appliance makers together to create a more powerful international group.
After being snubbed in July, Mr Webber said Pifco had returned with an informal approach via adviser Goldman Sachs after UK Active Value revealed its hand. "We believe there is good commercial logic and synergy in putting the companies together on an agreed basis," he said.
"We don't wish to enter a hostile or contested bid situation. It's not our style."
This weekend Kenwood again denied that a formal offer had been made. "If there had been ... Kenwood would have reported it to shareholders," a spokesman said. "We have no great fight with Pifco. It's just that we don't see the logic."