The three clubs have all made poor starts to the season, with Bournemouth the only one of the trio to currently be sitting outside of the drop zone.
However, Thompson fears that the Cherries will be caught by the end of the season, as he believes that Newcastle United will have enough to get out of trouble.
“I know Sunderland won last week but it was against 10 men so I don't see it changing much and I can see them still being down there,” he said.
“Aston Villa can't defend, they can't score goals, so they look like they'll be in trouble.
“Then there's Bournemouth, who were probably already a lot of people's bets to be down there, but I think having long-standing injuries, basically one key player in each department, has done it for them. Then they've got Artur Boruc in goal making mistakes, so it doesn't bode well for them this season.”
Sunderland have appointed Sam Allardyce in the hope of avoiding the trapdoor which leads to the Championship, and they have improved under the 60-year-old’s leadership so far.
Villa have also recently sacked their manager, and they are on the look out for a new man to take charge, following Tim Sherwood’s dismissal.
Bournemouth, meanwhile, are likely to stick with Eddie Howe regardless of how their season plays out – but they do face a tough test, competing in England’s Premier League for the first time in their history.
At the moment, out of the three clubs, Villa are in the most trouble – as they are already four points adrift of safety, and that gap could increase further by the time they are in action against Tottenham Hotspur on Monday evening.