Cornick, 21, has been on loan to Leyton Orient already this season where he made 13 appearances and scored once.
Quigley, 20, played three games for the Gills earlier this season before he suffered a cruciate ligament injury, but has been allowed to return.
"The pair know each other really well, they have a great understanding on the pitch," Gills boss Ady Pennock said.
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Bournemouth have loaned winger Harry Cornick and striker Joe Quigley to Gillingham until the end of the season.