Boris Johnson has made his second surprise visit to Kyiv since Russia began its invasion of Ukraine.
The Prime Minister told President Volodymyr Zelensky that Britain could train up to 10,000 troops every 120 days, when the two men met during an unannounced visit by Mr Johnson to Kyiv on Friday.
No 10 said international partners would be invited to host the programme, if the offer is accepted by Ukraine.
In a statement, Mr Johnson said: "My visit today, in the depths of this war, is to send a clear and simple message to the Ukrainian people: the UK is with you and we will be with you until you ultimately prevail.
"As Ukrainian soldiers fire UK missiles in defence of your nation's sovereignty, they do so also in defence of the very freedoms we take for granted.
"That is why I have offered President Zelensky a major new military training programme that could change the equation of this war – harnessing that most powerful of forces, the Ukrainian determination to win," he added.