The Merseysiders have struggled with their defence this season, particularly at set-pieces, and have conceded 32 goals in 23 league games.
Thompson believes that Potters centre-half Shawcross should be on the agenda of Jurgen Klopp and made a transfer priority in the summer.
He told Sky Sports: "When Liverpool evaluate at the end of the season and look at the sort of goals they conceded, I wouldn't be averse to see them looking towards Shawcross as a solution.
"In fact, I think he would be absolutely ideal and he's been one of the most underrated centre backs over the last five seasons.
"You just have to look at Stoke's stats with and without him."