Deputy Chief Constable Iain Livingstone told a meeting of the Scottish Police Authority board that around 5,000 officers will be required for the president's visit, which is expected between 12 and 15 July.
But despite having to cancel rest days and rearrange shift patterns, Mr Livingstone said his force had yet to receive official confirmation that the visit will go ahead or whether it will receive any financial support from the UK Government.
He said: "I have to stress that we do not have any final confirmation that the president of the United States will actually include any specific engagements in Scotland. However, we do have to prepare for such an eventuality. I have, therefore, established an appropriate command and planning structure..."
Asked how much he thought the policing operation would cost, Mr Livingstone said he estimated it would in the region of £5m.
He added: "That is a key concern of mine and the organisation. (A figure) around the £5m mark is clearly a significant impact on an already disciplined and focused budget.
"We don't have any clarity at this stage if at all about where additional funding could be sought. I have not had it clarified about President Trump's visit."