As per Chris Wheatley (Arsenal reporter for Football London), the two London clubs are keeping tabs on the England playmaker.
According to the report, Arsenal manager Mikel Arteta is a huge fan of Maddison and wants him at the Emirates. However, the report also claims Arsenal are aware of Maddison's lofty price tag, which could be a sticking point in negotiations.
Chelsea, meanwhile, view Maddison as a potential replacement for Hakim Ziyech. The Blues are yet to decide on the future of the Moroccan, who struggled in his debut campaign at Stamford Bridge.
Chelsea and Arsenal target James Maddison urged to stay at Leicester
Manchester United were previously interested in signing Maddison, but the Leicester City star stayed put. The Englishman was advised by former Leicester manager Micky Adams to remain with the Foxes and avoid leaving for Old Trafford.
"Leicester have shown in terms of wages and ambition that they're as good as anyone. Maddison would have to go to Manchester City or Liverpool to improve on what he's got at Leicester."
"As a young man he's just got to keep developing his game and working hard. He must not listen to the hype or get ahead of himself. That's the time it bites you on the backside as a footballer."
Steve Nicol echoed Adams' comments, saying a move to Manchester United would not benefit Maddison.
"Under normal circumstances this would be kind of a no brainer, somebody like him, playing at a provincial side shall we call them in Leicester City. The big guns of Manchester United come calling for you and it's only a matter of, can the two clubs sort it out financially?
"That's what used to happen. The bottom line is, is it going to benefit this guy going to United right now? I don't think it would. I think it would help him to keep playing in the way he has at Leicester."
Maddison has been one of Leicester's standout players ever since his arrival from Norwich City in 2018. The 24-year-old scored 11 goals and provided 10 assists in all competitions this past season, playing a key role in Leicester's fifth-place finish and FA Cup triumph.
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