The Match of the Day host tweeted directly to Cowell to ask for the shows to be aired at different times in December.
"Be a lovely gesture and mark of respect to our wonderful athletes if X Factor didn't run against SPOTY. What do you think @SimonCowell?" Lineker tweeted.
Lineker later revealed that ITV had stated that the two programmes will not be scheduled at the same time.
He retweeted a message from The Mirror journalist Mark Jefferies: "Good news @GaryLineker and sport fans,I've been told by ITV spokesman there's "no chance" X Factor will clash with SPOTY."
In past years, the Sports Personality of the Year ceremony has gone up against The X Factor, leading to reduced ratings for both programmes.
Andy Murray, Mo Farah, Bradley Wiggins, Ellie Simmons and Jessica Ennis are among the stars who are tipped to win this year's Sports Personality trophy.