Lawrence, 21, came up through the ranks at Manchester United, but left last summer in order to join Leicester City after impressive loan spells with Carlisle United and Yeovil Town last season.
The Welshman, who can play out wide, up front or as an attacking midfielder, has played just 51 minutes of Premier League football though, and enjoyed a productive loan stay with Rotherham United earlier this season, notching one goal and one assist in six appearances for the Millers.
They report that Bournemouth, Ipswich, Wolves, Blackburn, Charlton, Leeds, Bolton, Rotherham and Wigan Athletic have all been snubbed by the Foxes as they attempt to snap Lawrence up today.
Leicester boss Nigel Pearson reportedly wants Lawrence to remain in his squad for the final weeks of the season, as they battle relegation from the Premier League.
Leeds have been lacking a winger in recent weeks and it seems that manager Neil Redfearn saw Lawrence as a potential solution to that problem, but must now look for other targets with Lawrence staying at the King Power Stadium.