According to Catalan newspaper SPORT, Barcelona are desperate to add new players to their squad in January, and Barcelona have liked Ziyech for a while.
Barcelona even enquired into signing him while he was still an Ajax player.
The report adds that Chelsea would be open to letting Ziyech go on loan with no obligation to buy.
However, the main stumbling block for Barca is his high wages, with Ziyech allegedly earning €7 million per year at Chelsea, which is a big problem for the Spanish club given the financial issues that they have faced in recent years.
While Borussia Dortmund have also made an offer, Ziyech is waiting for Barcelona to make their own bid.
Ziyech has managed to get in the Chelsea squad recently, but it has mainly been down to injuries to the likes of Mason Mount, Romelu Lukaku and Timo Werner, with Thomas Tuchel preferring those three options ahead of the Moroccan.
The 28-year-old has barely played since arriving from Ajax in 2020, and he could move permanently in 2022, as he searches for more game time.
This season, Ziyech has played in 10 games in all competitions, scoring twice and also providing an assist, and while he has shown signs of promise, he has largely been underwhelming in a blue shirt.