Although recent developments in DNA sequencing have allowed for great leaps in both the quality and quantity of genome assembly projects, de novo assemblies still lack the efficiency and accuracy required for studying genetic variation of individuals. Thus, efficient and accurate methods for calling and genotyping genetic variants are fundamental to studying the genomes of individuals. We study the problem of genotyping insertion variants. We assume that the location of the insertion is given, and the task is to find the insertion sequence. Insertions are the hardest structural variant to genotype, because the insertion sequence must be assembled from the reads, whereas genotyping other structural variants only requires transformations of the reference genome. The current methods for constructing insertion variants are mostly linked to variation calling methods and are only able to construct small insertions. A sub-problem in genome assembly, the gap filling problem, provides techniques that are readily applicable to insertion genotyping. Gap filling takes the context and length of a missing sequence in a genome assembly and attempts to assemble the intervening sequence. In this paper we show how tools and methods for gap filling can be used to assemble insertion variants by modeling the problem of insertion genotyping as filling gaps in the reference genome. We further give a general read filtering scheme to make the method scalable to large data sets. Our results show that gap filling methods are competitive against insertion genotyping tools. We further show that read filtering improves performance of insertion genotyping especially for long insertions. Our experiments show that on long insertions the new proposed method is the most accurate one, whereas on short insertions it has comparable performance as compared against existing tools.