The 18-year-old made 18 appearances for Ronald Koeman's side during the 2020-21 campaign, but his current deal at Camp Nou is due to expire next June.
Barcelona have left the teenager out of their first-team squad for pre-season amid the uncertainty surrounding his future, with Manchester United said to be admirers.
According to Mundo Deportivo, there is also serious interest from Man City and Chelsea, with the two sides 'willing to push hard' for the midfielder's signature in the current market.
The report claims that Barcelona have offered Moriba a new five-year deal but are yet to receive a response, and Koeman's side are now 'running out of patience'.
The youngster's wage demands are thought to be making it difficult for the Catalan giants, who are struggling financially amid the coronavirus pandemic. body check tags ::