The US President is due to visit his golf course at Turnberry which regularly hosts the Open where he is expected to join up with his son Eric.
The two are expected to be holding private meetings with business figures who have been flown in for private meetings with the President.
Former Ukip leader Nigel Farage and a source close to Boris Johnson have told the Daily Express that they will not be meeting the President this weekend.
However, there is speculation that Mr Farage, who is close to the President, will meet him on a trip to Washington next week.
Mr Trump has made it clear that he has refused to meet with Ms Sturgeon in a move which will strike a chord with many people in Scotland and the rest of Britain who are angered by the divisive politics of the SNP.
In response SNP deputy leader Keith Brown is leading a protest against Mr Trump in Glasgow while Ms Sturgeon is heading a gay pride march.
According to reports, Mr Trump spends phone calls to Theresa May “bitching” about the First Minister.
Ms Sturgeon has been a vocal critic of Mr Trump’s policies and it is understood he flatly rejected meeting the SNP leader during his three-day stay.
Mr Trump used to be close to the SNP.
While Ms Sturgeon was deputy leader to Alex Salmond the SNP Scottish Government overturned planning rules to allow the US billionaire to build another golf course in Aberdeenshire.
An unnamed former Number 10 adviser told the Huffington Post: “He totally hates Nicola Sturgeon. He spends lots of his time bitching about Sturgeon. He loathes Salmond too.
“But why spend so much time talking about Sturgeon in a phone call with Theresa May?”
A Tory source today said of the claims: “Whatever Nicola Sturgeon says, this will be a blow to her ambitions of being seen as a global stateswoman.
“Like everyone else, the US president can probably see she’s a separatist with no intention of running a productive and responsible government.”