Only Liverpool have managed such a feat, winning it four times in a row from 1981-1984, so Pep Guardiola's men will hope to close in on that record.
Here, the PA news agency looks at City's run, Liverpool's feat and Aston Villa's record in this competition.
Chasing the trilogy
Guardiola won his first trophy in English football when City won the 2017/18 Carabao Cup. After edging past Bristol City in the semi-final, Guardiola's side were far too strong for Arsenal at Wembley as they won 3-0 thanks to goals from Sergio Aguero, Vincent Kompany and David Silva.
They followed it up with another success 12 months later as Chelsea were beaten 4-3 on penalties after a drab 0-0 draw remembered best for Blues goalkeeper Kepa Arrizabalaga refusing to be substituted.
This year City have again taken the competition seriously, getting past Preston, Southampton, Oxford and a two-legged semi-final with Manchester United to again reach the final.
Last time Liverpool were top of the pile in English football they dominated the League Cup with a run of four wins in the 1980s. In 1981 they beat West Ham 2-1 in a replay, then downed Tottenham 3-1 12 months later before the hat-trick was completed in 1983 with a 2-1 win over Manchester United. The fourth came in with a 1-0 replay victory over Everton at Maine Road.
Aston Villa will always be synonymous with the League Cup as they won the first ever edition, beating Rotherham over two legs in 1961. They won it twice more in the 1970s and two times in the 1990s, beating Manchester United and Leeds in the space of three years. Villa are tied with Chelsea and United on five titles and will draw level with City on six if they can upset the odds at Wembley.