Klose was on target for Joachim Low's men on Friday, equaling Gerd Muller's national record of 68 goals for the Nationalelf in a 3-0 win over Austria.
That result put the team on the brink of qualification for the finals in Brazil and Tuesday's away match could push it 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 has yet to win a game in qualification.
Low's side unsurprisingly heads into the contest as a heavy favorite, having not lost a game in World Cup qualification since a 5-1 defeat to England in 2001.
Germany has not tasted defeat in qualification for any major tournament since 2007 - when the club was beaten 3-0 by Czech Republic - and boasts a five-point lead over Sweden at the the top of Group C following the success over Austria.
The three-time World Cup winner has scored 25 goals from just seven qualifiers so far, and will be confident of increasing that total against a Faroe Islands side that has already conceded 22 times in a dreadful campaign.
Lars Olsen's men did find the net in their encounter with Kazakhstan, taking the lead through Frodi Benjaminsen.
However, the team's lack of defensive stability again proved to be to its 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 the team 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 Sept. 2012 and, although Faroe Islands does have home advantage, it will come as no surprise if Low's charges produce a similar result in Torshavn.
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