Speaking to BBC Newsbeat in West Sussex earlier, Sir Keir said the current system was “unfair and ineffective”.
In response, the government said there were lots of opportunities for students to access higher education and support.
‘Work in progress’
It comes after Sir Keir said university would be out of reach for him if he was applying as a student today and the cost of living crisis was holding young people back.
“We do need to change that and we will come up with a fairer package for students that helps them with the money they have to outlay,” he said.
Newsbeat spoke to him at a seaside cafe in Worthing and asked what that system would look like.
But he didn’t give any details, adding: “That’s work in progress.
“It will be a fairer system but on a wider package, how do we get our energy bills down, how do we get our food bills down, how do we ensure our economy is actually booming and people feel like they’ve got money in their pocket again.”
Many teenagers got their results last week but rules around student finance differ depending on a variety of things – like where you’re studying in the UK and what subject you pick.
But tuition fees vary between the nations, costing £9,250 a year in England, £9,000 in Wales, £4,710 for Northern Irish students in Northern Ireland and free for the majority of Scottish students in Scotland.
Sir Keir said the cost of living crisis is impacting on people’s day-to-day lives but also “on the longer term decisions, particularly of young people”.
“One of the worries I have now is because the government has failed so badly on the economy, for many young people they’re holding their results but their hopes and aspirations are being held back,” he said.
“Increasingly young people are feeling they’ve got to stay near home so they can stay living with their parents because they can’t afford it – that’s holding them back.”
Responding to Sir Keir’s comments that he would not be able to afford university, Education Secretary Gillian Keegan told the BBC he “doesn’t need to worry”.
“I have been working on degree apprenticeship routes for lots and lots of different occupations and one of those now includes a lawyer,” she said.
Student loans are made up of a loan for tuition fees, which have been capped until next year at £9,250 a year, as well as a means tested loan which covers accommodation and living costs.
“We have also got a £276m hardship fund which will be given out by universities,” Ms Keegan said.
“So if anybody does feel that that’s holding them back, then that option is there.”
Newsbeat also asked Sir Keir whether he was a fan of Taylor Swift after recent reports that Prime Minister Rishi Sunak went to one of her gigs during his US holiday.
He didn’t reveal whether he was a Swiftie but did admit to being a fan of Stormzy – who’s previously backed ex-Labour leader Jeremy Corbyn.
And he even turned into a bit of a music critic when he described the rapper’s This Is What I Mean album as “really fantastic”.
“I think it’s very different to some of the stuff he did before. It was really brave to go out in a slightly different way,” he said.
Sir Keir says he planned to see Stormzy live months ago, but couldn’t after one of his kids tested positive for Covid.
“That’s the one that we want to get back in the diary as soon as we can.”