The actress, who plays Rachel Breckle, revealed that she has been in contact with the Star Trek icon since writing to him at drama school.
She told Inside Soap: "I keep trying to persuade Patrick to star in Emmerdale!
"When I got my place at drama school, I was looking for a bit of advice about where to get funding, so I wrote to Patrick and Sir Tom Courtenay, who are connected with my local area. Bizarrely, they both wrote back and have become mentors to me."
Stewart has appeared in a soap once before, playing a fireman on Coronation Street in 1967, when he extinguished flames at number 9 caused by Dennis Tanner.
Oaten further divulged that Billy Liar actor Courtenay has praised her performance on Emmerdale.
"Tom watched the show the other night," she added. "He emailed me and said, 'That's our girl, very well done - very proud!' It was so nice."
Gemma Oaten joined Emmerdale just over a year ago, becoming involved in Ashley's elder abuse storyline earlier this year, and now being pregnant with boss Jai Sharma's baby.