Conte ideally wants two players for each position which means Chelsea could sign Rudiger, stick to their plan of loaning out Kurt Zouma, and still have room in the squad for another centre back after selling Ake and allowing John Terry’s contract to expire.
Virgil van Dijk and Leonardo Bonucci are Conte’s top central defensive targets, while Jerome Boateng is thought to be keen on a return to England.
But with deals for all three of those men likely to be difficult, Chelsea have moved for Rudiger to make sure they are not left short in defence when the season starts.
Rudiger’s agent has travelled to England and, despite trying to negotiate a price closer to £39m, Roma expect the 24-year-old to join the Premier League champions.
Chelsea acted quickly after the collapse of the proposed transfer of Kostas Manolas to Zenit St Petersburg earlier this week.
Having initially made a check on Manolas, Chelsea instead decided to use Roma’s need to sell players to comply with Financial Fair Play to move for Rudiger.
Chelsea have tracked the Germany international for some time and believe the player can be a good signing for the future and the present.
Rudiger is currently part of the Germany team preparing for Sunday’s Confederations Cup final against Chile and is happy to play anywhere across the centre of defence.
His arrival would give Conte the option of switching to a back four and restoring Cesar Azpilicueta to right-back.