The Reds, under Croatia manager Zlatko Kranjcar, are positioned 247th, with 76.5 points, up three places in the latest IFFHS Club World Ranking.
Iran's Sepahan, coached by Amir Qalenoi, also moved up seven places and stand in the 295th place on 68.5 points, followed by the Tehran-based Esteqlal in the 330th with 65 points.
Another Iranian soccer team Zob Ahan also moved up 19 places to arrive at 336 on 64.5 points.
Manchester United has remained in first place with 317 points, followed by Chelsea and FC Barcelona.
The top 20 teams in the latest IFFHS rankings:
(number in parenthesis indicates last month's rank)
1.( 1.) Manchester United
2.( 4.) Chelsea FC
3.( 2.) FC Barcelona
4.( 5.) Hamburger SV
5.( 3.) FC Shakhtyor
6.( 7.) SV Werder Bremen
7.( 8.) Arsenal FC
8.( 6.) Club Estudiantes de La Plata
9.( 9.) Cruzeiro EC Belo Horizonte
10.(11.) Galatasaray SK Istanbul
11.(10.) AS Roma
12.(13.) Gremio Foot-Ball Porto-Alegrense
13.(12.) Olympiakos Pireas
14.(19.) FC Twente Enschede
15.(44.) Liga Deportiva Universitaria de Quito
16.(14.) FC Bayern Munchen
17.(18.) Liverpool FC
18.(15.) FC do Porto
19.(20.) FC Internazionale Milano
20.(29.) Sevilla FC