Liverpool are currently two points clear of Manchester City at the top of the Premier League, although Pep Guardiolas side have a game in hand.
Klopps side must also beat Porto if they want to reach the last four of the Champions League.
United, meanwhile, are in the battle for third and fourth place in the Premier League, while in Europe, they face a tricky test against Barcelona.
Should Liverpool and United both progress in the Champions League, it has already been confirmed that they will face each other in the semi-final.
But Carragher has urged Klopp to prioritise the Premier League – even if that results in United gaining an advantage in Europe.
I think the big decision both managers have, or certainly Jurgen Klopp will have, is the Champions League semi-final, Carragher told Sky Sports.
Pep will still go strong on that.
It will be a big thing – what will Jurgen Klopp do in a big semi-final with a league game coming?