Speaking to Sky's Wilfred Frost on his The Master Investor Podcast, Nick Clegg said the UK needed to "think long and hard" about "whether we've overdone it" with freedom of speech laws.
Other candidates are racing to catch up ahead of a crunch deadline on Thursday - but there is concern about the logistics of a key hustings event in which contenders will make their pitch to undecided voters.
The Brexit vote was largely driven by concerns about immigration, with voters buying the promise by the Leave campaign to "take back control". But as numbers soar, it's once again become the public's top issue - overtaking the economy.
Government policy post-Brexit has been the driving force behind the number of people moving to Britain in recent years - and while the numbers crossing on small boats are relatively small, those too are at record highs.
The Immigration Debate, hosted by Sky News' Trevor Phillips in front of a live audience, will take place in Birmingham at 7pm on Wednesday 10 September.
The education secretary, who is running to be Labour's deputy leader, seeks to allay concerns about ministers' commitment to the bill sparked by Angela Rayner's exit.
The notes allegedly written by Lord Mandelson, one of which describes the convicted paedophile as his "best pal", suggest a closer relationship than has previously been acknowledged.