In his interview with Bauer and Global radio station, Mr Corbyn was asked what he would do with regard to Scotland were he to become Prime Minister: "I'll obviously open discussions with the government in Scotland and listen very carefully to what the Scottish Parliament says", he said.
The SNP leader has previously called for a second vote on Scotland's constitutional future between autumn 2018 and spring 2019.
Speaking to Sky News in Moray in Scotland, Scotland's First Minister repeatedly refused to say if a promise of another Scottish referendum would be a precondition of any deal.
"The key point of principle for me is clarity at the end of a process to allow people to make a genuinely informed choice about the future of our country".
Sturgeon pointed to other times May has changed her mind.
Scottish Government proposals to keep the United Kingdom in the single market were "brushed aside" by the Prime Minister, she added.
She added: "This election offers people the opportunity to give [the proposals] democratic legitimacy and make it impossible for the prime minister to continue to ignore Scotland's voice".
"I think the referendum should take place, if there is to be one, after the Brexit negotiations are concluded because this is the most important thing".
Les Français votent, vers un raz-de-marée REM — Législatives
Le tout, sur fond d'abstention record, avec environ un électeur sur deux qui ne s'est pas déplacé pour voter. En revanche, l'ex-Premier ministre Manuel Valls a annoncé être " nettement en tête " dans l'Essonne.
The slaughter of music fans in Manchester on Monday jolted the election debate on to a new course, placing the issues of security, extremism and community cohesion front and centre.
The SNP will today launch their election manifesto in the full knowledge that for them, the only way is down.
Meanwhile Ms Sturgeon, whose 2015 success was partly down to Labour voters backing the SNP, will try to stop the tide flowing back to Labour by warning a vote for Mr Corbyn's party risks "letting Tory MPs in by the backdoor". "They are political dogma - an ideology".
"We already have a pledge to increase the NHS budget by 2 billion pounds by the end of this Scottish Parliament", she said.
Nationalist MPs at Westminster would also support the reversal of the two-child cap on tax credits, with Ms Sturgeon pledging: "We will campaign tirelessly against the immoral rape clause that goes with it - a policy that shames every Tory candidate who supports it".
Rennie, however, accused the SNP leader pretending "she is interested in Europe" when in fact she only cares about independence.
"We will not follow the Tories in their blind pursuit of a pre-election surplus to spend in five years time, or Labour in their reckless plans to hike taxes without knowing if they will secure any additional revenue".
"This was a exhausted manifesto launch by a First Minister who has failed in this campaign to give people a single, positive reason for voting for her party".
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