The Ukraine president and UK prime minister were speaking at a press conference on Wednesday as Zelenskyy made an historic visit to the UK.
During a speech in Westminster earlier, Zelenskyy had pleaded for “wings for freedom” in the form of fighter jets.
The UK has so far refused to supply planes, arguing it would take years to train pilots to use the sophisticated F-35s and Typhoons in RAF service.
At the news event in Dorset, Sunak insisted “nothing is off the table” when it comes to support for Ukraine. His remark came after it was earlier revealed Sunak has asked the defence secretary, Ben Wallace, to explore what could be provided.
But after the prime minister said it would take three years to train a Typhoon fighter pilot from scratch, Zelenskyy told journalists: “I didn’t even know it takes three years to train a pilot like that.
“Come on, we will be sending you pilots who have already trained for two and a half-years.”
The West had hesitated providing Ukraine with battle tanks, before Germany and the US finally agreed to send their coveted armaments in a watershed move.
A similar stand-off is now taking place over planes, with Zelenskyy’s pleas so far being resisted.
At the press conference, both Zelenskyy and Sunak acknowledged the decision on jets requires involvement from Nato allies.
Zelenskyy said: “When it comes to Typhoons, not everything depends just on the decision of Great Britain.
“I will be working in that direction because this is how we have been able to change many things.
“We are intensifying our diplomacy and I do believe within a day we will be able to meet with a dozen EU leaders and then we will go back home.”
At the press conference, the prime minister said: “When it comes to fighter combat aircraft, of course they are part of the conversation — indeed, we have been discussing that today and have been previously.
“That’s why we have announced today that we will be training Ukrainian air force on Nato-standard platforms, because the first step in being able to provide advanced aircrafts is to have soldiers or aviators who are capable of using them.
“That is a process that takes some time. We’ve started that process today, that’s because we are keen to support the president and his country in delivering a victory.
“And nothing is off the table and our leadership on this issue is something we all collectively should be very proud of, and I know the president is grateful for.”
The Ukrainian president acknowledged discussions had been “fruitful”.
Nato is anxious about further escalating tensions between the world’s two biggest nuclear powers – the US and Russia – and edging everyone closer to the “World War III” scenario many fear.
Russia’s embassy to Britain on Wednesday warned London against sending fighter jets to Ukraine, saying such a move would have serious military and political ramifications for the entire world, Reuters reported.