The former Liverpool defender has also backed Newcastle United and Watford to retain their top-flight status for the 2016-17 campaign.
“Villa are gone and then, although they had a good result on Monday Night Football, I think Swansea will join them,” Thompson told Sky Sports.
“Jonjo Shelvey is a great signing for Newcastle and just what they needed given their lack of creativity elsewhere. He could well be the difference between Newcastle staying up and Swansea going down.
“Watford also need to be careful but I think Sunderland are just too vulnerable defensively and will complete the trio.”
A footnote added: “Thommo predicts: Aston Villa, Swansea and Sunderland.”
Villa are at the foot of the Premier League table at the moment with just 12 points from 22 matches.
Sunderland are second from bottom in the standings with 18 points from 22 matches, while Newcastle are a place above them with 21 points.
Swansea City are 17th with 22 points, while Norwich and Watford are 16th and 12th with 23 and 29 points respectively.
It is hard to call the bottom three, although Villa do indeed look set for the drop to the Championship.
In Sam Allardyce, Sunderland have a manager who knows how to keep teams up, and perhaps that could make a major difference for them.
Newcastle have a team good enough to finish in mid-table and have severely underperformed so far this season.