The offer from Stamford Bridge was not expected to be increased significantly, as Chelsea are reluctant to move beyond the 8m-pound mark given Xhaka will turn 34 in September. Even so, club officials still view the fee as reasonable value for a player with his experience and leadership qualities.
Chelsea's recruitment strategy this window includes the pursuit of a seasoned Premier League midfielder, and Xhaka has been identified as a strong fit for that requirement. His profile and top-level pedigree continue to appeal, even if negotiations have not progressed.
Sunderland, however, are in no financial need to sell and remain in a strong position to resist approaches.
The club are also aware that Xhaka is open to the idea of a reunion with Xabi Alonso, under whom he previously lifted the Bundesliga title during his time at Bayer Leverkusen, adding another layer of complexity to the situation.
The Swiss international still has two years remaining on his Sunderland contract and remains a central figure in their plans. He captained the side to a seventh-place Premier League finish and secured Europa League qualification in their first season back in the top flight, underlining his importance to the squad.
Xhaka departed Bayer Leverkusen in July last year after 99 appearances for the German club, following a highly successful spell.
Prior to that, he enjoyed the longest stretch of his career at Arsenal, where he made 297 appearances between 2016 and 2023, establishing himself as a key figure in English football.