There has been no club-to-club contact, and the Black Cat would not welcome any offers, with the midfielder currently not for sale.
Xhaka is among several experienced Premier League-proven options being considered by Chelsea, who are prioritising leadership in midfield.
The Swiss international turns 34 in September, meaning the Blues would be unwilling to pay over the odds for a deal.
Sunderland signed him for £13m last summer, and he played a key role in helping them retain their Premier League status after promotion.
According to Sky Sports, Xhaka remains highly valued at the Stadium of Light, especially after previously attracting interest from West Ham before opting against a move back to London.
New Chelsea manager Xabi Alonso, who begins work next week, previously enjoyed success with Xhaka at Bayer Leverkusen, where they won the Bundesliga together.