Gou -- who gave up Foxconn's management reins four years ago -- announced in August his intention to run in Taiwan's January presidential elections.
The 73-year-old needs to gather 290,000 signatures by Thursday to qualify as an independent candidate.
Prosecutors in western Yunlin county said they had questioned 13 people and raided several locations on Wednesday over suspected bribery in Gou's signature campaign.
Four suspects offered a carton of toilet papers worth around Tw$900 ($28) to staff of a farmers' association in exchange for each signature, according to prosecutors.
Under Taiwan's election laws, bribing people to sign or not sign for a potential candidate is punishable by a maximum seven-year jail term, in addition to a fine of up to Tw$10 million.
The case is among around a dozen investigations launched over Gou's signature campaign, local media reported.
Prosecutors in the capital Taipei said on Wednesday that they were investigating two bribery cases connected to Gou's signature campaign.
A total of 13 suspects were questioned on Tuesday and released on bail, according to Taipei district prosecutors' office, without elaborating on the allegations.
Gou's campaign office announced on Thursday that over 1.03 million signatures were filed.
In China, Foxconn is under tax and land probes in several provinces, Beijing's state-run Global Times reported last month.
The investigations come as self-ruled Taiwan -- which China claims as its territory and has vowed to seize one day -- prepares to hold presidential elections on January 13.
Officials from Taiwan's ruling Democratic Progressive Party, including its presidential candidate and Vice-President Lai Ching-te, have defended Foxconn and accused Beijing of trying to interfere in its elections.
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