Partey has been one of Arsenal’s top targets for the summer window but the Gunners have been unable to reach an agreement with Atletico Madrid.
Arsenal have already offered Matteo Guendouzi plus €25 million (£22.7m) for Partey but Atletico have rejected that bid and will only sell if the midfielder’s €50m (£45.5m) release clause is met.
According to Sky Sports, Arsenal are now looking at alternatives and Jorginho is on the Gunners’ shortlist.
The 28-year-old was linked with a move away from Stamford Bridge at the end of last season after he was left on the bench by Frank Lampard for four consecutive games.
But the Italy international has started both of Chelsea’s Premier League fixtures this season and scored a penalty in the 3-1 win over Brighton last week.
Jorginho then missed his spot-kick on Sunday as Chelsea were beaten 2-0 by Liverpool at Stamford Bridge.
Chelsea have plenty of competition for places in midfield but Frank Lampard is expected to trim his squad before the window closes on October 5.
Ross Barkley and Ruben Loftus-Cheek have attracted interest from West Ham and Aston Villa, who are keen on loan deals.
Arsenal, meanwhile, are also targeting Lyon’s Houssem Aouar and have also offered Guendouzi to the French club in exchange for the midfielder.
But Lyon rejected the proposal and are demanding €60m (£54.7m) for the 22-year-old.