The newspaper ceased publication, alongside its sister title the Daily Sport, when its owner Sport Media Group went into administration.
It is not thought the Daily Sport will return, but Sullivan, through newly formed Sunday Sport (2011) bought the Sunday Sport and its intellectual property.
A holding page for the newspaper has been set up at Dailysport.co.uk, stating that it will return this Sunday (8 May).
It stated: "It had looked like Sunday Sport had become history after Sport Media Group went into administration.
"But tycoon David Sullivan, who founded Sunday Sport in 1986, moved and bought the title, saving an institution as British as the morning cuppa or fish and chips."
The website also states that, for the first time in its 25-year history, the newspaper will be printed full colour.
Publisher Trinity Mirror has confirmed to PrintWeek that it will print the title at its Watford, Oldham and Glasgow facilities.
Sunday Sport (2011) was formed on 15 April, Sullivan was appointed as director on 19 April.
A statement from administrator BDO Stoy Hayward said: "The administrators continue to welcome interest in the Sunday Sport’s sister publication, the Daily Sport, and the companies’ other publications."