An increasing number of pulsar wind nebulae (PWNe) are being identified in the TeV band by ground-based Imaging Air Cherenkov Telescopes such that they constitute the dominant source class of Galactic TeV emitters. However, MeV–GeV PWN counterparts are still largely lacking. To date, only a dozen PWNe are identified by the Fermi–Large Area Telescope (LAT) in the MeV–GeV band. Most PWNe are located along the Galactic plane embedded within the prominent, diffuse Galactic γ-ray emission, which makes these sources difficult to disentangle from the bright diffuse background. We present a systematic search for γ-ray counterparts to known PWNe in the 300 MeV–2 TeV energy band using the Fermi–LAT. We target the locations of previously identified PWNe that lack detected Fermi–LAT pulsars to minimize associated pulsar contamination. The sample includes six previously identified Fermi PWNe and eight Fermi–LAT sources associated with PWNe. We report the analysis of 58 regions of interest and classify Fermi–LAT detected sources as either a likely PWN or a candidate PWN counterpart based on their morphological and spectral characteristics across the broadband spectrum. There are nine unidentified Fermi–LAT sources that we consider as likely PWN counterparts, which, if confirmed to be PWNe, would greatly increase the PWN population detected by the Fermi–LAT from 12 to 21. The remaining Fermi–LAT detected sources are considered weaker PWN candidates. A second approach in the systematic search for γ-ray emitting PWNe will involve studying the off-pulse phases of Fermi–LAT detected pulsars for the presence of an obscured PWN and will be reported in a subsequent paper.