The League One outfit are expected to be busy in the transfer market before the start of the new campaign, which begins on the first weekend in August.
Reports had suggested that it was only a matter of time before Evans completed a switch to the Stadium of Light after falling out of favour at the Royals.
However, according to Roker Report, the deal is now off the table despite the former Manchester City trainee having agreed personal terms with the Black Cats.
The report suggests that while the 23-year-old was prepared to make the switch to the North-East, the player would like to try to remain in the Championship.
Evans made just four starts for Reading during the closing two months of the last campaign.