Borrell acknowledged on Monday that any transfers wouldn't come from the EU itself, but would instead be donated by individual EU countries.
The representatives from the Polish and Slovakian governments did not respond to the request, while the Prime Minister of Bulgaria rejected it.
The pilots of Poland and Slovakia wouldn't need much training if the planes were transferred.
In a move likely aimed at increasing pressure on Europe to act, the Ukrainian parliament on Monday said that Europe was sending 70 fighter planes to Ukraine, including 28 from Poland, 12 from Slovakia and 16 from Bulgaria.
The fighter plane drama came on top of a flurry of announcements over the weekend that saw European leaders promise a flood of new weaponry for the Ukrainian military to assist in fighting off invading Russian troops.
The U.S. and European powers are pushing weapons into the country by road because of the closed air corridors.
The first countries to send supplies to the Ukrainian border were Poland, Estonia and Latvia.
On Monday, Finland announced it would join the club and give weapons and supplies to Ukraine. Sweden will deliver 135,000 field ration, 5,000 helmets, body armor and 5,000 anti-tank weapons.
The Canadian Foreign Affairs Minister is going to Poland Tuesday to coordinate the shipment of 100 Carl Gustaf anti-armor rocket launchers, along with 2,000 munitions and other aid.
She told reporters before the trip that lethal aid would be sent to Ukraine. My role is to make sure that the aid is given to the Ukrainian soldiers who are fighting for their country. I was able to get an agreement from Poland to make sure that that delivery could be done through their borders.
One of the biggest surprises in recent European political history was the announcement by the German Chancellor that he was sending weapons to the Ukrainians. He promised an immediate $100 billion injection into the German military.
Up to $350 million worth of weapons from the U.S. were to be released to Ukraine on Friday. There will be capabilities in there to help them with both their ground defensive capabilities as well as airborne defensive capabilities, according to a senior U.S. Defense Department official speaking with reporters at the Pentagon Monday.