Fabrizio Romano has reported that Xhaka himself is driving the move, a development that follows Sky journalist Florian Plettenberg's revelation that personal terms between the player and Chelsea have already been agreed.
Chelsea submitted an opening bid of £8m for the 33-year-old, which Sunderland rejected, having informed the west London club that no offer would be accepted regardless of its size. Chelsea are expected to continue their attempts to reach an agreement during the coming week.
Xhaka joined Sunderland from Bayer Leverkusen a year ago and has been one of the club's most important players since. He registered one goal and six assists in 34 Premier League appearances last season, starting 32 of them. His contract on Wearside runs until the summer of 2028.
Chelsea's desire to reunite Xhaka with former Bayer Leverkusen manager Xabi Alonso, who oversaw the midfielder's best performances before leaving to take the Real Madrid job, has been the driving force behind the approach. Sunderland's firm position means the path to a deal remains unclear, but the player's willingness to push for the move gives Chelsea reason to persist.
For Sunderland, the situation is genuinely difficult. A player who has been instrumental in everything positive about their return to the Premier League is now pushing to leave, and the club's public stance that he is not for sale at any price may be tested by the combination of a higher bid and a player who has made his intentions clear.
Whether Chelsea's next offer — which is expected during the coming week — is significant enough to change Sunderland's position will likely determine how this situation develops. The club cannot force Xhaka to stay if his mind is made up, but they are not required to sell at a price they consider inadequate either.