The three men – Sheikh Salman al-Ouda, Awad al-Qarni and Ali al-Omari - are being held on multiple charges of terrorism.
They will be convicted and executed after the end of Ramadan next month, the Middle East Eye reports, citing two government sources and one of the men’s relatives.
Saudi authorities have not commented on the report.
Adam Coogle, Middle East researcher at Human Rights Watch, said he could not confirm the report, but told The Independent: “What I can say is that Saudi prosecutors are seeking the death penalty against these men merely for their alleged peaceful political affiliations and opinions."
He added: “We see this as a clear departure from past practice and an indication of just how much the repression level has increased since MBS [Mohammed bin Salman] became crown prince nearly two years ago.”
Mr Odah, who is known for his comparatively progressive views on Sharia (Islamic law) and homosexuality, was arrested in September 2017 after tweeting a prayer calling for reconciliation between Saudi Arabia and Qatar after Riyadh launched a blockade against the emirate.
Mr Qarni is a preacher and author while Mr Omari is a broadcaster.
They were also arrested in September 2017.
“They will not wait to execute these men once the death sentence has been passed,” one source told Middle East Eye.
Dana Ahmed, Amnesty International’s Gulf researcher, told The Independent: "The Saudi Public Prosecution’s recurring calls for the death penalty in the case of a number of individuals being held for peacefully exercising their rights to freedom of expression - including Sheikh Salman al-Ouda - raises real alarms for the fate of detained activists and religious clerics in the country.
"We’re calling on the Saudi Arabian authorities to immediately release those detained solely for peacefully exercising their rights to freedom of expression, association and assembly, and to drop any charges against them."
Another Saudi government source told Middle East Eye the execution of 37 Saudis for terrorism offences in April was used as a “trial balloon” to gauge the strength of international condemnation.
Responding to the April executions, Human Rights Watch described the punishment as “grotesque” while Amnesty International called it “a chilling demonstration of the Saudi Arabian’ authorities callous disregard for human life”.