"We don't think it's right that they send us the refugees, they need to be stopped on Serbian territory," Hungary's Prime Minister Viktor Orban said in a radio interview.
"We take every option into consideration, including the possibility of complete physical closure of borders," Orban said, adding that a decision could be made next Wednesday.
Serbia is not yet a member of the EU, though it has started membership talks, while Hungary is part of the Schengen zone.
So far this year, some 54,000 migrants have entered Hungary, and the total this year is expected to be up to 130,000.
Orban's comments came amid an anti-immigration campaign involving billboards with slogans such as, "If you come to Hungary, you cannot take Hungarians' jobs."
At the same time a poll in April said that xenophobia has reached a 14-year high while the anti-immigration Jobbik party has seen its poll ratings rise.
