The 20-year-old Republic of Ireland international joined the Tigers on an initial one-month deal at the start of November and has made six appearances for Steve Bruce's side as they look to secure promotion back to the Premier League after a three-year absence. His final match will now be the trip to Blackpool on January 1.
Brady, who scored one and set up a further two on his international debut against Oman back in September, spent the 2011-12 season on loan at the KC stadium, making 41 appearances for the Tigers, scoring three times. Hull are currently fifth in the table, five points off the top two spots.
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Attacking midfielder Lingard, 19, has made four appearances while at the King Power Stadium.
Centre-half Keane, also 19, returned to his parent club after sustaining a hamstring injury during his Foxes debut at Bolton Wanderers but is close to full fitness.
Both will now be available for home games against Barnsley, Cardiff City and Huddersfield Town - along with away trips to Millwall, Hull City and Burnley.