Swinney spoke to the incoming US President via a phone call in December though the issue of trade tariffs was not directly discussed.
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Swinney was asked about relations with the new US administration as he appeared on BBC Scotland’s Sunday Show.
He said Trump was “very warm and positive” on the call and spoke of his enthusiasm for Scotland, where he has family roots and owns two golf courses.
Tariffs on whisky, a vital Scottish export, were not discussed as Mr Swinney said he did not want to go into that detail without knowing the President’s precise plans.
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The First Minister said: “He talked warmly about his mum’s roots in Lewis and his pride in the business interests that he’s taking forward at Turnberry and at Balmedie – the golf courses.
“So he’s got an affinity and a warmth towards Scotland and if that means that it helps us to avoid tariffs that might be damaging to legitimate and important, critical economic interests in Scotland, then don’t be surprised if this First Minister in Scotland uses that channel to try to secure that outcome.”
Mr Swinney previously backed Kamala Harris to win the presidency, something which the Republican’s son Eric Trump criticised during a visit to Scotland.