Activists raised over £16,000 to make the balloon and gain permission to fly it over Parliament Square.
Sadiq Khan and City Hall gave the go-ahead for it to be flown on Friday during the Stop Trump protest.
Activists are now trying to get the balloon to Scotland to coincide with his trip there on Saturday.
The petition said that organisers had emailed National Air Traffic Control, the Civil Aviation Authority, the First Minister and the Chief of Police in Scotland.
It added that because of airspace restrictions, the protesters need flight clearance to fly the blimp near the President's golf course in Turnberry.
More than 6,300 people have signed the petition so far.
According to the Guardian, the protest team will board a sleeper train to Glasgow with the balloon and travel to Turnberry.
On the way, they will pick up more helium to enable it to fly, the newspaper reports.
Mr Trump is visiting his golf course in Turnberry, Scotland as part of his UK visit.
His family has links with Scotland. Mr Trump's mother was born on the Isle of Lewis before moving to New York at the age of 18.
It is thought that he will spend much of his time in the country playing golf.
