Whitbread was due to train with the Rams on Monday morning and he looks likely to make his debut for Derby against Ipswich at Pride Park on Tuesday night.
The Rams, who sacked manager Nigel Clough on Saturday evening just hours after defeat to Nottingham Forest, have problems in central defence following Richard Keogh's red card at the City Ground.
Keogh is suspended for the visit of the Tractor Boys while Shaun Barker and Mark O'Brien are still making their way back from long-term injuries.
Meanwhile, Leicester are currently spoilt for choice in the centre-back department with club captain Wes Morgan and Liam Moore in excellent form, signings Marcin Wasilewski and Ignasi Miquel waiting in the wings, and Sean St Ledger close to returning from a knee injury.
Whitbread, 29, who started his career at Liverpool and played for Millwall and Norwich before joining Leicester in the summer of 2012, has made just four appearances for the Foxes this season - the last being in the 5-2 victory over Carlisle in the Capital One Cup last month.