The 'Don't Cha' singers - who are set to go on the road to showcase their new album 'Doll Domination' - would love the Formula 1 driver, who is currently dating Nicole Scherzinger, to join them.
Melody Thornton said: "There is always room for him on the tour bus. He is a very sweet and good person."
Nicole, who began romancing Lewis after the pair met at the MTV Europe Music Awards in Germany in February, revealed she is smitten with the 23-year-old driver but admits it is difficult to date a fellow celebrity.
She told Britain's Daily Mail newspaper: "The attention we get isn't important to me. As long as my boyfriend and I are happy that is all I care about. And we are truly happy.
"It is hard to have a relationship in this industry, so we are taking things one step at a time and living moment to moment. As long as the other girls are OK about it, I hope he will come on tour with us."
Earlier this month, 30-year-old Nicole confessed her boyfriend's fast driving "terrifies" her.
She said: "I'm actually terrified when he takes me on a drive. Especially through the canyons in Los Angeles. Wow! He's at one with his car - let's just say that!"