The Germany centre-back had rejected Chelsea's previous offer worth around £140,000-a-week.
Rudiger is seeking £200,000-a-week and is using the interest of several clubs as a bargaining chip.
It is believed foreign clubs would be able to offer packages in the range of £400,000-a-week, including bonuses.
However, there is growing confidence within Chelsea that a deal can be struck with the important defender.
The Daily Mail says the Blues are opening up negotiations with an improved contract offer somewhere around Rudiger's initial demands.
As well as a base salary of £200,000-a-week, the new contract will include a number of bonuses and incentives to boost Rudiger's bank account.
Rudiger is comfortable at Stamford Bridge and loves playing under compatriot Thomas Tuchel.
But knowing this could be his last big contract, the former Roma man is determined to get as much money as possible.
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