With the arrival of Jose Mourinho at Old Trafford, many of the world's best players are already being linked with moves to Manchester United.
The newspaper understands that the Portuguese will be given a transfer kitty of around £200 million, and around a quarter of that figure would be needed if they were to attempt a move for the 22-year-old England international.
United had the joint best defensive record in the league last season, although that was arguably down to the performances of goalkeeper David de Gea, who once again proved his worth to the Manchester club.
Daley Blind was impressive in the centre-back position while Chris Smalling produced a string of dominating performances, and the two forged a sound partnership. The problem has been that when one of those two players were absent through injury or suspension, there was no one of ample quality to step in and deputise.
Should a move come to fruition, the acquisition of Stones would certainly address this key area of the pitch that needs strengthening.
The problem for United will be the competition they are sure to face for the signature of Stones, with the newspaper also reporting that Chelsea remain interested, following on from having three bids rejected for the Everton man last summer.
Stones is currently on duty with the England national team as they continue their preparations for this summer's European Championships.