Everton value centre-back Jarrad Branthwaite at more than £70m having rejected an opening bid from Manchester United.
One source suggests the offer from United was £35m plus add-ons, some way short of Everton's price for the 21-year-old, who is believed to be in a similar transfer bracket to defenders Josko Gvardiol, Harry Maguire and Wesley Fofana - all of whom were sold for higher fees.
Everton regard Branthwaite as a key player and intend to keep him this summer.
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However, director of football Kevin Thelwell admitted last month that players will be sold this summer as Everton attempt to improve their financial condition to stay in line with Premier League Profit and Sustainability Rules.
Branthwaite played 35 times for Everton in the Premier League last season although was cut from England's Euro 2024 preliminary squad.
Recruiting in the heart of defence has been marked as a priority for FA Cup winners Manchester United this summer.
Raphael Varane is leaving at the end of the month when his deal expires, while Jonny Evans has been offered a contract to stay on at Old Trafford.
Another Everton player who could fetch a sizeable fee is Amadou Onana - but no move has yet emerged for the midfielder.
When does the summer transfer window open and close?
The 2024 summer transfer window in the Premier League and Scottish Premiership is officially open.
The window will close on August 30 at 11pm UK time in England and at 11.30pm in Scotland.
The Premier League and Scottish Premiership brought forward Deadline Day to link up with the other major leagues in Europe. The closing dates were set following discussions with the leagues in England, Germany, Italy, Spain and France.