Stones has been the subject of two bids from the London club, with Everton recently declining an offer of £26 million.
More offers are likely to come from Chelsea but Everton and Stones must not be lured into a transfer.
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Everton must not sell
With the influx of TV money into the Premier League, Everton are in a much better financial position then they have been in the past where they needed to sell in order to raise finances.
The transfers of Wayne Rooney in 2004 and Mikel Arteta in 2011 being the prime examples. If the 21-year-old centre back is sold this would signal a complete lack of ambition by the football club and could lead to their talented cohort of younger players questioning their future at the club also.
Instead the Merseyside club should be looking to the future and building their team around the likes of James McCarthy, Romelu Lukaku and Stones himself.
The Barnsley born centre-back is seen by many as the epitome of a well-grounded guy who goes about his business with minimal fuss. However, there is no doubt that even he could get his head turned by the West London club and serious consideration of their interest will have to be taken.
It must also be said though that there has been no direct quote by Stones himself about wanting to leave Everton and he has put in some good defensive performances in Everton's last four pre-season games suggesting he is quite content at Everton.
John Terry has been quoted recently as saying he aims to stay at Chelsea for at least two more years, add to this the likes of Gary Cahill, Kurt Zouma and Branislav Ivanovic who can also play in Stones' position and this would suggest that he would have to settle for a considerable number of matches on the bench.
Whereas, if he was to stay at Everton for a few more years he could learn much from his partnership with England international Phil Jagielka and gain valuable Premier League experience week in week out.
One thing not on Everton's side is the media's quest to make football into an oligopolistic game where only the elite should survive. This is the type of transfer the media love, a bright, young English talent being touted by a big money move to a "bigger" club.
However, one definite thing that will not happen is Everton will not be bullied into any potential transfer as was seen in the summer of 2013 with Manchester United's "derisory and insulting" combined moves for Marouane Fellaini and Leighton Baines. Fellaini did end up leaving but the £27.5 million fee was very much on Everton's terms.
It is important for Everton to keep a talent such as Stones and fend off Chelsea as it not only shows a signal of their intent to fight off the big guns and compete in the higher echelons of the league.
But also for other clubs who could perhaps find themselves in Everton's position and if Everton hold firm, this could show that they can fend off the elite clubs in the league and make the Premier League a more competitive place.