Riyad Mahrez is undoubtedly one of those, scoring once again as the Foxes won away to Everton at the weekend.
French website Foot7 are reporting that he is the subject of a £29.9 million offers from both Manchester United and Tottenham Hotspur.
Mahrez has already addressed the speculation, via his agent, who said, reported by The Express, that the Algerian has no intention of leaving Leicester in January.
With Leicester currently top of the Premier League, the only way is down this season if he joins another side, and neither United or Tottenham could offer him Champions League football.
What Leicester are currently achieving is so rare in English football, for an unfancied and unbacked side to upset the 'elite', and they are proving no flash in the pan.
Mahrez owes it to himself to continue his journey and see just how far this incredible Leicester team can go.
Here is a look at how supporters responded to speculation linking him away...