The Lazio star can break Gerd Muller's all-time international goal tally of 68 should he find the net on Tuesday against a side yet to win in qualification
Klose was on target for Joachim Low's men on Friday, equalling Gerd Muller's national record of 68 goals for the Nationalelf in a 3-0 win over Austria.
That result put them on the brink of qualification for the finals in Brazil and Tuesday's away match could push them over the line.
Toni Kroos and Thomas Muller also found the net in that triumph, but the onus will likely be on Lazio striker Klose, who has the chance to make history against a Faroe Islands outfit that have yet to win a game in qualification.
Low's side unsurprisingly head into the contest as heavy favourites, having not lost a game in World Cup qualification since their 5-1 defeat to England in 2001.
Germany have not tasted defeat in qualification for any major tournament since 2007 - when they were beaten 3-0 by Czech Republic - and boast a five-point lead over Sweden at the the top of Group C following the success over Austria.
The three-time World Cup winners have scored 25 goals from just seven qualifiers so far, and they will be confident of increasing that total against a Faroe Islands side that has already conceded 22 times in their dreadful campaign.
Lars Olsen's men did find the net in their encounter with Kazakhstan, taking the lead through Frodi Benjaminsen.
However, their lack of defensive stability again proved to be to their downfall as Kazakhstan produced a second-half comeback to take the points.
It has been four years since Faroe Islands' 2-1 win over Lithuainia, which marked the last time they took maximum points from a World Cup qualifier, and Olsen's men look unlikely to break their duck in this game.
Germany cruised to a 3-0 win in the reverse fixture in Hannover in September 2012 and, although Faroe Islands do have home advantage, it will come as no surprise if Low's charges produce a similar result in Torshavn.