The 24-year-old actress portrays Demelza Poldark in the hit BBC series alongside the actor who is among those tipped to replace Daniel Craig as 007.
Asked if she would be up for competing with Turner for the role, Tomlinson told the Press Association: “Sure why not? I’ll take him for a run for his money.”
Joking that he could then become her Bond girl, she added “wouldn’t that be funny?”.
Craig is the second longest serving Bond, having taken up the role in October 2011.
His last outing as Bond was in 2015’s Spectre, but shortly after its release he said he would rather “slash my wrists” than appear in another film as the secret service agent.
Tomlinson and Turner have also worked together on a Vincent van Gogh biopic - This Is Vincent.
She said: “It’s so funny we seem to take the same jobs.
“I love working with Aidan, he’s an amazing actor and such a nice person.
“When we both took This Is Vincent neither of us knew the other was in the cast list but we didn’t see each other during filming.
“We already see quite a lot of each other so I think I can cope with one day when we’re not on together.”
Tomlinson was speaking as she teamed up with train ticketing company Trainline and revealed herself as a big fan of rail transport.
“I’m not a train spotter but I do take a lot of trains. I go up north a lot because I’m originally from Yorkshire so I teamed up with Trainline.”