The Merseyside club has endured difficult results of late, coming under criticism after losing 2-0 to Leicester City in the EFL Cup earlier this week.
Prior to the defeat at the King Power Stadium, Liverpool were held to home draws against Burnley and Sevilla, and fell to a 5-0 defeat at Manchester City earlier in September.
Despite their current struggles, Thompson does not believe that Klopp's suitability for the job should be getting questioned, insisting that the German is in the process of building the team.
"There's no debate, he should not be under pressure," the 63-year-old told Sky Sports News.
"I would like to think he's building a side now. I believe they are better now [than under Brendan Rodgers]. The defensive side of things has been Liverpool's Achilles heel, not just through Klopp's reign, but we had the same thing with Brendan.
"I love the way he plays," he added. "Yes, he's got his problems but at the moment I don't see anyone anywhere near Jurgen Klopp, and that's the problem. Who would Liverpool go for? Who would they bring in [instead]? These people who are questioning Klopp, I'm not hearing anybody come up with a solution to it. There shouldn't be any debate about his position at Liverpool."
Liverpool take on Leicester at the King Power for the second time this week in Saturday afternoon's Premier League clash in the East Midlands.