But Derby could face competition from Brighton and another, previously unlinked club in Aston Villa, who are next in the running with the bookmaker - albeit as 8/1 outsiders.
That the pair were below Sunderland [8/1, now 16/1] on Monday is certainly intriguing, given that neither club has been credited with interest in the meantime.
Brighton have been linked with a number wide players this summer, while one of their own, Jamie Murphy, is a target for several clubs, according to Sky Sports News.
And the Seagulls should have little trouble meeting Leicester's asking price for Lawrence - said to be £7 million [The Sun] - especially if they can offload Murphy, for whom it is claimed they will consider offers of £4 million.
Aston Villa have also been tipped to add to their wing options, although the seemingly imminent arrival of Ahmed Elmohamady from Hull City could satisfy Steve Bruce's need in that area.
Hull City's Ahmed Elmohamady
Lawrence, whose contract expires next summer, scored 11 goals and created as many in 36 games on loan to Ipswich Town last season.
When asked if Lawrence could return to Portman Road this coming campaign, Town boss Mick McCarthy told the BBC: "I think Tom will have his heart set on the Premier League" - which could rule out Derby County and Aston Villa.
Where will Lawrence end up - Derby, Brighton, Aston Villa or other?
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