It is the third loan deal this season for Osborn, 22, following spells at Hayes & Yeading United and Maidstone United.
The former Dagenham & Redbridge player has featured five times for the Fleet this season, scoring twice in the Kent Senior Cup, to bring his club total to 11 goals in seventy-four games.
He first joined the club on loan from Dagenham in 2013, making the move to Stonebridge Road permanent the following season.
Concord almost sealed a loan deal for Osborn this time last season but that move fell through because of injury. However, the Essex club have returned for the player this month and he will join them for a second spell in a run of fixtures that includes games against Gosport Borough, Truro City, Dartford and Oxford City.