Oriol Romeu returned to Camp Nou over the summer from Girona, but the La Liga champions are short of genuine options at the base of their midfield.
According to ESPN, Bayern Munich's Joshua Kimmich is hugely admired by Barcelona, but a deal for the Germany international at this stage is complicated due to his asking price.
The Catalan outfit's financial problems have therefore forced them to look elsewhere, and both Jorginho and Thiago are viewed as genuine options to move to the club next year.
Jorginho only has a contract at the Emirates Stadium until next June, but he has been a regular this season, featuring on eight occasions in all competitions.
The Italy international is unlikely to sign a new deal with the Gunners, though, meaning that he could be available on a free transfer next June.
There have also been suggestions that Jorginho could be available for the right price in January, with Juventus thought to be keeping a close eye on his situation.
Arsenal would allegedly be prepared to let the 31-year-old move to Turin if they were able to sign French midfielder Adrien Rabiot in exchange.
Thiago is in a similar situation at Liverpool, with the Spaniard only having a contract until next June, and he is being heavily linked with a departure.
The 32-year-old has not made a single appearance for the Reds this season due to a hip problem which he initially suffered in April.
Liverpool boss Jurgen Klopp is said to be keen for the club to hand the midfielder a new deal, but senior figures at Anfield are thought to have a different view on the
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