The Reds have made a promising start to their title challenge following sixth successive victories in the opening two months of the season.
Liverpool FC were 3-0 winners against Southampton at Anfield last weekend to move to two points clear of Manchester City and Chelsea FC.
The Merseyside outfit will make the trip to third-placed Chelsea FC at Stamford Bridge in the Premier League on Saturday evening.
Klopp’s side reached the Champions League final last term before a 3-1 loss to La Liga giants Real Madrid in Kiev back in May.
The Reds were dramatic 3-2 winners against Ligue 1 winners Paris Saint-Germain in the Champions League at Anfield last week.
However, former Liverpool FC captain Thompson believes the Reds should focus on winning a first Premier League title.
“The priority, because of their start to the season, is winning the Premier League,” Thomspon told Sky Sports. “That should be the number one target.
“It is closely followed then by the Champions League.”
Liverpool FC appointed Klopp as their new manager in October 2015 following a poor start to the campaign under Brendan Rodgers.
The Reds signed Fabinho, Naby Keita, Xherdan Shaqiri and Alisson Becker in the summer transfer window.
Klopp hasn’t won silverware in his past two and a half seasons despite reaching Europa League, League Cup and Champions League finals.
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