It has been reported that the American businessman will soon complete the purchase of the revered South Ayrshire course, which has staged the Open Championship on four occasions and is due to host the competition within a few years.
Turnberry is the only course on the Open roster which is in private hands and it's owners Leisurecorp, a subsiduary of the Dubai Government, are known to be keen to sell.
Trump who already owns the Menie golf resort course in Aberdeenshire, has previously said he would not invest in Scotland again after falling out with the Scottish Government over plans to construct an offshore windfarm in Aberdeen bay.
However, it appears that the chance to get his hands on on a course due to host the Open has been too much to resist for the businessman, who owns 16 golf courses worldwide.
One source said: "The deal is not done yet, but it should be soon," while another figure in the world of golf added: "It's well known that Leisurecorp are looking to sell, so this [deal] is not out of the ballpark.
"And if you speak to anyone in golf, Trump has been looking for an Open course for a while, so this all makes sense."
Turnberry was bought by Leisurecorp from Starwood Hotels and Resorts in 2008, although the company was retained on a 50-year contract to manage the course and its facilities.
A spokeswoman for Starwood Hotels and Resorts said: "We can't comment on press speculation but should the estate change hands, then Starwood expect to continue to manage Turnberry under the Luxury Collection Brand, independent of any potential change in ownership of the estate and building.
"Should any sale of the asset be completed, existing relationship with clients, associates, suppliers and partners will remain unaffected. "We will work hard to ensure that unique guest experiences, for which the hotel is renowned, will continue to be offered to guests from around the world."