Sterling was joined in the top 10 by teammate Luis Suarez in fifth. Sterling provided an assist for Suarez to score his league-leading 30th goal.
Atletico Madrid remains second after it prepared for its Champions League semifinal against Chelsea with a 2-0 win against Elche to stay first in the Spanish League. Diego Simeone's side can win La Liga for the first time since 1996 if it wins its next three matches.
City rival Real Madrid is third, a point behind Atletico, after winning the Copa del Rey final against Barcelona. Gareth Bale, who won the copa with a fantastic solo goal, is runner-up to Sterling.
"Bale or Bolt? Stunning Welsh run to the goal and to the title of the King's Cup was a worthy bid to make history," Leonardo Bertozzi of ESPN Brazil said.
Edinson Cavani polled third, after scoring both goals in Paris Saint-Germain's 2-1 defeat of Lyon in the French League Cup final. PSG ranked fifth in the team vote, tied with Borussia Dortmund.
Juventus polled fourth after moving to two wins away from its 30th Serie A title with a 1-0 win at home against Bologna. Paul Pogba scored the winner, and was ninth in the player vote.
Lukas Podolski was fourth after finding his form in front of goal to boost Arsenal's bid for Champions League soccer. He scored four times in the games against West Ham and Hull.
Monteverde also praised the return to form of Bayern Munich, which polled seventh for reaching the German Cup final by beating Kaiserslautern 5-1, then host Eintracht Braunschweig 2-0 in the Bundesliga.
Last week's winner of the player vote, Marco Reus, tied for fifth with Suarez after his goal and performance in Dortmund's 4-2 win against Mainz. He was a place above teammate Robert Lewandowski, who also found the net.
Everton was seventh after beating Manchester United 2-0, and standout Seamus Coleman was voted in 10th. Bottom English side Sunderland drew with Manchester City and ended Chelsea's unbeaten home record under Jose Mourinho, and was 10th.
AP Global 10 rankings, week ending April 23
1. Liverpool, 111 points.
2. Atletico Madrid, 72.
3. Real Madrid, 71.
4. Juventus, 46.
5 (tie) Paris Saint-Germain, 45.
Borussia Dortmund, 45.
7 (tie) Everton, 42.
Bayern Munich, 42.
9. Roma, 35.
10. Sunderland, 32.
1. Raheem Sterling, 87.
2. Gareth Bale, 68.
3. Edinson Cavani, 39.
4. Lukas Podolski, 32.
5 (tie). Luis Suarez, 30
Marco Reus, 30.
7. Robert Lewandowski, 27.
8. Lionel Messi, 25.
9. Paul Pogba, 17.
10. Seamus Coleman, 16.