The Uruguayan's agent, Pere, is the brother of the former Barcelona boss, and Anfield officials fear the link will trigger the 25-year-old's exit.
Roman Abramovich wants Guardiola as his next manager, and dreams of linking Suarez with Atletico Madrid's prolific frontman Radamel Falcao - who is believed to be heading to Stamford Bridge in January.
Manchester City will rival Chelsea for the Liverpool star's signature, but the Blues are willing to match the reigning Premier League champions' salary offer, providing they can sell Fernando Torres.
Reds boss Brendan Rodgers will be determined not to lose Anfield's leading marksman, but even the £50million price-tag hanging over the South American's head is unlikely to put Abramovich off.
Meanwhile, Guardiola is currently enjoying a year-long sabbatical after leaving the Nou Camp in May, and despite strong interest in his services, the Spaniard is refusing to discuss his future until Christmas.
Roberto Di Matteo is merely seen as a stop-gap for Chelsea and Russian owner, Abramovich, with the Italian tactician's stock taking another blow yesterday following a 2-1 Premier League defeat against West Brom at The Hawthorns.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms