The Foxes are ODDS-ON favourites at 1/5 to capture the attacking midfielder before the transfer window slams shut.
Tottenham and West Ham are joint second favourites at 5/1 to land the Monaco star.
It's believed the Belgium international would be leaving the Ligue 1 side on loan for the remainder of the season.
The Foxes have stolen a march in the race and are in advanced talks as they are set for a loan swap with flop Adrien Silva going in the opposite direction.
And Monaco boss Leonardo Jardim is determined to work with Adrien Silva again after previously working together at Sporting Lisbon.
Paddy Power: Youri Tielemans' next club
Leicester – 1/5
Tottenham – 5/1
West Ham – 5/1
Arsenal – 7/1
AC Milan – 20/1
Barcelona – 20/1
Tielemans joined Monaco from Anderlecht two years ago in a £21million move Anderlecht two seasons ago.
Spokesman Paddy Power said: “Monaco have put Tielemans on the market at the last minute ahead of Thursday’s deadline day closure.
“Which kind of sounds a bit like a supermarket trying to flog off the dodgy cuts of meat at the end of the day. At the minute, Leicester are our odds-on favourites to sign him, though there could be a battle for his signature over in North London.”
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