The news comes as police chiefs warned that the threat of terrorism is "not diminishing".
"If the legislation is passed by Feb 27 we can prevent the automatic release of any further terrorist suspects who might pose a threat to the public", the source said.
Kahn was arrested in 2017 and given a four-and-a-half year sentence in May 2018 after pleading guilty. They can be recalled to serve the remainder of their sentences if they break the law.
The Streatham attack was the second lone Islamist-related terror attack in London in the past three months. The UK's fear risk level is at present set at "significant", which means an assault is likely.
Sudesh Amman was shot dead by police after embarking on a stabbing spree in Streatham High Road, south London, on Sunday afternoon. He was put under 24-hour police reconnaissance on his discharge after it is comprehended security administrations viewed him as an "amazingly concerning a person".
Instead, the parole board will carry out a risk assessment, he said.
"Part of the solution must be ensuring those who pose the greatest threat to our society are removed from it, and so my colleagues and I are supportive of the Government's plans to strengthen our ability to keep the most risky terrorists locked up for longer".
The bill, announced earlier this week following the Streatham terror attack, would prevent the early automatic release of terrorists now in prison.
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The Whitehall official said the attack in Streatham highlighted an issue surrounding terrorists with relatively short prison sentences.
'Be that as it may, with 3,000 or so subjects of intrigue as of now on our radar, and many indicted psychological militants soon due to be discharged from jail, we basically can't observe every one of them, constantly'.
But the schedule could be tight, with just three days planned to get the Bill through the upper House of Lords. "We can not continue to be in a position where the state has no power to block the release of terrorists who continue to pose a threat".
According to right-leaning think-tank the Henry Jackson Society, a number of convicted extremists may be due for release in March.
In November, a man who had been automatically released halfway through a 16-year sentence stabbed two people in central London before he was shot by police.
A statement released by the jihadist group through its media outlet Amaq, said the man answered its call to attack civilians in nations opposing IS.
"This is in relation to release arrangements which are part of the administration of a sentence and it would be our position that you can change those without being considered to breach an offender's human rights". Lawyers, including a former government adviser, have warned that blocking early releases could lead to legal challenges from inmates.