Labour has already been forced to quietly drop its hopes of a renegotiation of the trade deal in 2025 because of opposition in the EU.
It is instead focusing on boosting defence and security ties in the immediate aftermath of an election win, which is seen as more realistic.
But Mr Sarwar said: “We have to fix the mess of Brexit that has been created by the Conservative Party, we have to reset the relationship with our partners and friends in the European Union.
“When I’m talking to sister Labour parties across the UK, when I’m talking to ambassadors for individual countries across the union or I’m talking to EU representatives, they aren’t actually asking Labour to commit to rejoin the European Union at this election campaign.
‘We can build on alignments’
“What they’re asking for is to commit to change the relationship, to reset the relationship and that’s exactly what we’re going to do.”
Mr Sarwar said that Labour was “going to look at where alignment works for us and is in our national interest and we can look to build on those alignments”.
He predicted EU member states would look at a Labour government and “recognise that these are people we can work with”.
In addition, he said the Scotland Office would do much to promote “high-quality Scottish products abroad”, such as smoked salmon and whisky.
The Scottish Tories were approached for comment.