Toto Wolff is keen for Valentino Rossi and Sebastien Ogier to take part in promotional tests for Mercedes.
Three-time MotoGP champion Jorge Lorenzo had a test in the team's 2014 car at Silverstone this year, the Spaniard labelling it "a dream come true".
Lorenzo's lap times were reportedly competitive and Rossi, who has seven premier class titles in MotoGP to his name, has previously tested for Ferrari.
Ogier, a four-time World Rally champion, has never driven a Formula One car.
But Wolff, head of Mercedes-Benz motorsport, told La Gazzetta dello Sport: "I am aware that our sport is also a show. I'd really like to test the skills of Rossi and Ogier in our cars.
"The idea would be to organise a track day with both of them."