Liverpool have won each of their six Premier League matches this season, and host Chelsea on Wednesday night in their opening Carabao Cup fixture.
Thompson admitted Klopp will likely make changes for the game, but that realistically the German should be targeting the trophy as he is yet to add to Liverpool's collection since taking over in 2015.
Ahead of the game, the pundit said: "It would be great, I would love to do it and it's a trophy.
"Jurgen has to win a trophy this year. For the quality of squad he now has, he has to win a trophy.
"It gives him a great opportunity and I would gladly take the Carabao Cup, but you have to look where your priorities lie, which is what most managers do and make changes in these early rounds.
"Dare I say it, a lot of managers over the years, in the big six clubs, have put out weakened teams thinking if they do get knocked out they will take it on the chin and it will give them a better chance in Europe and the Premier League.
"They obviously don't want to go out at the early stage, it's not very nice, but come later in the season they will view it as a godsend.
"There could be a multitude of changes, but I think Jurgen Klopp has a great opportunity to change his team.
"He has been so consistent with his selections so far in the Premier League and Champions League and now he has a great opportunity to give the other players a run out.
"Xherdan Shaqiri will probably play and we are looking at such a good squad now that he could literally pick a second team of what we call star names. Nathaniel Clyne, Dejan Lovren, Joel Matip, Alberto Moreno and Fabinho should all start.
"Naby Keita will probably play, then there's Divock Origi and Dominic Solanke if fit, plus Daniel Sturridge. It's a decent team.
"What I would certainly hope is for Jurgen to have the cavalry on the bench, a lot of the first-team players."