The Stamford Bridge club saw an initial £8million offer turned down on Saturday, with Sunderland regarding the valuation as insulting. Sunderland have insisted their 33-year-old skipper is not for sale this summer.
However, Xhaka is keen on being reunited with his former Bayer Leverkusen boss, Xabi Alonso, and Chelsea are ready to return with another offer. The size of the second bid has not been disclosed, though Chelsea felt their initial offer was fair and close to Xhaka's value.
Chelsea's interest in Xhaka has largely been driven by Alonso, whose four-year contract at the club officially began on July 1. Together, Alonso and Xhaka won the Double with Bayer Leverkusen in 2023-24, claiming the Bundesliga and DFB-Pokal.
Sunderland signed Xhaka from Leverkusen last summer in a deal worth £13m, plus £4m in add-ons.
As captain, he helped Sunderland secure European football in their first season back in the Premier League, and he is contracted until 2028.
The former Arsenal midfielder, who turns 34 in September, is currently away with Switzerland at the 2026 World Cup.
Sunderland's stance reflects the importance Xhaka has held since his arrival, having gone straight into the role of captain and helped guide the club to a European return at the first attempt back in the top flight.
Chelsea, meanwhile, appear prepared to test that resolve again, banking on the personal pull of working under Alonso once more to help force through a deal before pre-season begins in earnest. The rejection of the opening bid has not deterred Chelsea, who view Xhaka as a key target given his existing relationship with their new manager.
Xhaka's experience and leadership qualities, demonstrated during his debut season as Sunderland captain, are understood to be significant factors behind Chelsea's persistence in pursuing the deal.
Sunderland will be reluctant to lose their captain so soon after his impact helped secure a swift return to European competition, adding further complexity to any negotiations between the two clubs.