A defence deal would pave the way to greater UK involvement in EU-wide defence research and joint procurement projects, as well as potentially unlocking full British access to a €150bn EU loans scheme announced last month.
But there have been reports that EU countries, notably France, want to link the wider reset talks to negotiations over fishing arrangements that are due to expire in June next year under the post-Brexit trade deal.
Brussels is also reportedly keen for the UK to agree a new youth visa deal, despite Labour previously ruling out the UK taking part in an EU-wide scheme.
Asked whether a row over fishing could hold up a defence pact, Kallas, who took up her current EU role in December, said: "Fish apparently are very important also when it comes to diplomatic relationships".
The former Estonian prime minister added: "I'm actually surprised at how important the fish are, considering the security situation".
"But I am definitely pushing this from my side, because I think the UK is a very important defence and security partner.
"It's the most logical defence and security partner that we have, and it's a beneficial relationship for both sides."