Metro reports that both clubs had scouts to watch the 19-year-old in action over the weekend.
Moore is regarded as one of the best young defenders outside of the Premier League.
The England Under-19 star has also been linked with the likes of Tottenham, Everton and Aston Villa.
Leicester reportedly want around £5million for the youngster.
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.