The actress is said to have enjoyed a number of dinner dates with the End of Watch actor at his West Village apartment in New York, according to Grazia.
The pair were allegedly introduced to each other by Holmes's former Dawson's Creek co-star Joshua Jackson.
Holmes was previously spotted attending Gyllenhaal's Broadway play If There is I Haven't Found it Yet in September 2012.
"Josh has been the mastermind behind this romance," a source told the magazine.
"Katie says that they have tons in common and Jake has already been to see her in Dead Accounts, plus she has been over to his apartment in the West Village for dinner."
Katie Holmes has been single since her divorce from Tom Cruise was finalised back in August.
Her Broadway play Dead Accounts will come to a close after less than six weeks on January 6.
Tom Cruise was recently seen out on a date with a New York woman identified as Cynthia Jorge.