More than 500,000 people have signed the petition on the Parliament website calling for the billionaire businessman to be prevented from entering the country.
Mr Trump has attracted widespread criticism for his views on immigration including his call for a wholesale ban on all Muslims entering the United States.
Liberal Democrat leader Tim Farron said: “Banning Trump is not the answer. It’s just the kind of attention this publicity junkie would want.
“Get him over here and put him on a platform so his odious and, frankly, weird views can be shot down in flames.
“But the NHS, education and housing are three things which immediately spring to mind as topics which would be worthier of parliamentary debate.”
Petitions on the Parliament website which attract more than 100,000 signatures go forward to a committee of MPs which considers which should be debated in the Commons.