Starmer is set to sign a new deal with the European Union this week as he hosts the first post-Brexit EU-UK summit on Monday.
The London gathering with EU chiefs is aimed at agreeing steps towards a closer relationship between Britain and the 27-country bloc that it left five years ago after an acrimonious referendum.
Details of any deal have remained vague, and Minister for European Union Relations Nick Thomas-Symonds told the BBC on Sunday that they were still being worked out.
He said the Labour government was taking a practical approach "where it is in our national interest to align on common standards to make sure we get far easier trade, to mean that businesses... can start trading with the EU again".
Starmer has ruled out rejoining the customs union and single market but has suggested the UK is ready for regulatory alignment with the EU on food and agricultural products.
His Downing Street office said a deal would help UK producers "who face red tape and checks just to export to our nearest and biggest trading partner" and would drive down costs in the shops.
EU diplomats in Brussels have been working on getting Britain to keep its waters open for European fishermen in return for easing the checks on some food imports from the UK.
Conservative Party leader Kemi Badenoch said it "sounds like we're giving away our fishing quotas, becoming a rule-taker from Brussels".
Both she and the anti-immigration Reform UK leader Nigel Farage described the yet to be announced deal as a "surrender" and said they would ditch it if elected.
On the contentious issue of a youth mobility scheme, Thomas-Symonds told the BBC's Sunday with Laura Kuenssberg programme that it would have to be "smart and controlled".
The European Union is said to be keen on a scheme that would allow European 18- to 30-year-olds to study and work in the UK, and vice versa in the EU for young Brits.
Earlier this month, Reform UK made big gains in local elections, continuing the momentum it built up at last year's general election.
Badenoch said she feared any youth mobility scheme would reintroduce the EU policy of freedom of movement "by the backdoor".
Thomas-Symonds rejected the criticism, highlighting that the UK already had 13 youth mobility schemes with other countries.
"Nobody is remotely suggesting that that is freedom of movement with those countries, it absolutely isn't," he said.
Senior Conservative Party politician Alex Burghart, said that such a scheme flew in the face of public concerns about high levels of immigration.
"They want immigration to come down and if you have an uncapped youth mobility scheme, you're going to have much higher immigration," he told the BBC.
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