BBC Sport understands the signing-on and agent's fees demanded by Rudiger's camp have proved too steep for Chelsea.

"He informed me some days ago in a personal talk," Tuchel told Sky Sports.

Tuchel had hoped to keep Rudiger at Chelsea but the Germany international has been strongly linked with a move to Real Madrid.

"We gave everything and now we enter a situation where we can't fight any more because of the sanctions and now Toni will leave," Tuchel added, referring to the restrictions placed on the club while a new owner is sought.

"Our hands are tied. I don't know what would have been the outcome [without the sanctions]. That's his decision. It's not a nice one for us but we don't take it personally.

"He is a key figure and will stay a key figure for us. We will miss him a lot. He is a guy who gives people courage, who people are a bit afraid of. He plays 55 games a season for 90 minutes at an outstanding level.

"He was the top defender in the past one and a half years with me and I have nothing but respect for him."

Chelsea could also lose centre-back Andreas Christensen this summer.

Like Rudiger, who joined the Blues for an initial £29m from Roma in 2017, the Denmark international's contract is up at the end of the season and will be allowed to leave on a free transfer, with Barcelona agreeing a deal to sign the 26-year-old.

Chelsea's financial situation has been uncertain since owner Roman Abramovich put the club up for sale last month before being sanctioned by the UK government.

Three bidders are attempting to buy the club from the Russian billionaire for more than £2.5bn, with the hope that a preferred bidder can be selected this week.

But it is understood the contract offer to Rudiger was made weeks before the advent of the sanctions, which put player contract deals on hold until the end of May when the government is expected to issue the club with a special licence.