Assange, 47, remains in British custody after he was arrested at the Ecuadorian Embassy in London, where he was holed up for almost seven years after breaching bail in 2012 over fears that sexual assault allegations lodged in Sweden could ultimately lead to his extradition to the US to face trial over the leaking of secret government information.
In 2010, WikiLeaks dumped thousands of confidential documents covering everything from the film industry to national security and war.
Morrison has previously said Assange, an Australian citizen, would have consular assistance available to him but would not get "special treatment".
Shipton also expressed shock at seeing his son removed from the Ecuadorian embassy. "I saw him, the way they dragged him down the steps... He didn't look good."
In May 2017, Sweden's top prosecutor dropped the long-running inquiry into the sexual assault against Assange, which he has always denied.
Prosecutors in Sweden have since confirmed that, while the investigation has not been resumed, they are looking into the case.
On Saturday, over 70 lawmakers in the UK have signed a letter urging the Home Secretary to give priority to a possible Swedish extradition request.
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