The Hitch star is an avid fan of the Vera Drake moviemaker and has often expressed a desire to work with him on a film project.
Mendes has now revealed she sent him a note begging him to consider her, and she has been waiting eight years for the offer to come in.
She tells Britain's The Guardian, "If you see Mike Leigh, tell him Mendes really wants him. And I do a good cockney (London accent)... I sent him a note maybe like eight years ago, and I'm sure he had no idea who I was. And then I ran into him and he was lovely. So I just hope these last eight years I've maybe done something that he's liked or could see potential in, so we could possibly work together."