Speaking to Australia's Sunday Telegraph, Williams revealed that mutual friends she shares with Reichardt - among them director Todd Haynes and Sonic Youth's Kim Gordon - insisted the pair work together.
"I didn't know Kelly before we went to make the film, but there were all these friends trying to get me to do the movie," Williams explained.
"The casting director lives a few blocks from me in Brooklyn. We go to the same coffee shop and she would just sort of poke me every now and then and say, 'I really think you should see [Kelly's] movie, Old Joy... And Kim Gordon... was always saying, 'You and Kelly would really get along, she's really cool'.
"And then the script arrived. It was first sent to me in short story form, with a little note from Todd Haynes saying, 'Take a look. She's a dear friend. You guys should work together.'''
Reichardt praised her leading lady, adding: "Michelle has this amazing stillness. There's stuff going on inside. You can see it in her eyes.''
Wendy And Lucy, which centres on a woman driving to Alaska who breaks down in Oregon with only her dog for company, is released in cinemas this Friday.
> Click here for our review of Wendy And Lucy