Mansell, 55, won the Formula One World Championship in 1992 with Williams. His son Leo, 23, is thinking about a Le Mans Series programme for 2009 while Greg, 21, competed in the 2008 Atlantic Championship alongside his sibling.
Nigel and Leo Mansell tested a Ginetta-Zytek sportscar in Spain and Ginetta managing director Richard Dean said he was impressed - and asked the racing legend whether he would be interested in the 24 Hours.
"From the moment he strapped into the car he was unbelievable," Dean said of the former F1 star. "You could tell he wasn't there to cruise around.
"He was there to push and absolutely wrung the car's neck in the first few laps. He was so impressive and you can tell why he was something special behind the wheel in F1.
"I asked him about sharing a car with his kids and he didn't rule it out. I'm sure it's something the Le Mans organisers would jump at, given the publicity it would generate."
Mansell told Motorsport News earlier this year: "Le Mans is always a potential. We have had some overtures made to us - with my two sons and myself driving in the same team - and maybe one day that might come to fruition."
Meanwhile Peugeot recently tested Davidson, who competed in F1 this year before his Super Aguri team went bust, in their own sportscar.
Team manager Serge Saulnier indicated that the 29-year-old driver is one of a few options, but was upbeat about the Briton's chances.
"He is under consideration for a role with us next year," he told Motorsport News. "He tested the car for us and we have some other drivers to test.
"We need to see how many cars we will enter at Sebring and Le Mans next year before we decide anything.
"He did well. The target of this test was more for him to get the feeling of the car. He's now got a good idea of the car and the team, so he will know about us if we consider a collaboration."
The 24 Hours takes place on June 13-14, 2009.