Ainsworth was a strong contender for the vacancy on Wearside, and the Black Cats were granted permission to hold talks, but he now looks set to stay at Adams Park.
He is also being considered for the vacany at Championship side Millwall, alongside former Derby County boss Gary Rowett and current caretaker manager Adam Barrett.
Parkinson is set to take charge of his first game against Ainsworth’s Wycombe on Saturday.
Supporters are currently voting on proposals to sell a majority shareholding to American businessman Rob Couhig, something that Ainsworth has strongly supported publicly.
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Ainsworth says he is ‘fully focused’ on Saturday’s game.
“Sunderland are a huge club and I’m fully concentrated on Saturday’s game,” he said.
“I’m told there’s a lot of rumours and that’s flattering, because it shows we’re doing well. It would take something spectacular to take me away from here.”
“There are so many factors in that. My family, my work here, the vote. But we’re very proud of what we’ve got here. I’m Wycombe Wanderers manager and I want to give the best account of ourselves on Saturday.”
Wycombe currently sit second in the table, four points ahead of the Black Cats. They have played one game more, however.
Parkinson is understood to be on Wearside now and will take training ahead of the game at the weekend.