The Reds will earn a place in the last 16 if they avoid defeat at Johan Cruyff Arena on Wednesday evening.
If Jürgen Klopp's men lose in Amsterdam, they will require a point against Napoli at Anfield on November 1 to be certain of progressing.
Group leaders Napoli – who host Rangers for matchday five – have already sealed their place in the first knockout round.
If Liverpool fail to beat Ajax and the Serie A outfit claim three points against Rangers, then Luciano Spalletti's side will be confirmed as group winners.
The Reds can claim top spot in the section, and seeded status in the last-16 draw, if they better Napoli's results by four points in the remaining two rounds of fixtures.
Alternatively, that situation could be achieved if the gap between the teams remains three points after matchday five and Liverpool then beat Napoli by a margin of four goals or more in L4.
Third-placed Ajax must beat the Reds to keep their hopes of qualification alive, while Rangers have already been eliminated but are still able to finish in third position and claim a place in the Europa League's round of 32.