The club had won 12 in a row in 1990, the last time they took the title in England's top flight.
Liverpool have set a club record by recording their 13th straight league win, as the Reds defeated Burnley 3-0 at Turf Moor in the Premier League on Saturday.
The Reds have won every match in England’s top flight since a 0-0 draw with Everton on March 3.
They have now outdone a 12-game winning streak set in the old First Division between April and October 1990, with the 1989-90 season the last time the Anfield outfit won the league title.
This is also the second consecutive season the Reds have started with four wins in a row, something they have never achieved before.
They are the only club among the 91 in the top four divisions in English football to boast a 100% record so far this season, and their win keeps them two points ahead of Manchester City in the early-season table, heading into the international break.
The Reds have not lost since they went down 2-1 to Manchester City on January 3, a run of 21 games, which equals their longest such run under Klopp.