With Trump openly coveting the prestigious award, President Volodymyr Zelenskiy floated the idea in a briefing to reporters, two days ahead of the announcement of this year's winner, who would have been selected earlier in the autumn.
"If Trump gives the world – above all, the Ukrainian people – the chance for such a ceasefire, then yes, he should be nominated for the Nobel Peace Prize," Zelenskiy said in comments released Thursday.
"We will nominate him on behalf of Ukraine."
Zelenskiy has worked hard to win Trump's support, and appears to be making some headway.
Tomahawk missiles top Kyiv's wishlist of US weapons that it believes can inflict serious damage on Russia and force it to the table.
Trump, who has expressed frustration with Russia's Vladimir Putin, has signalled he is open to providing them.
Trump has said he deserved the Nobel award, given to four of his White House predecessors, for what he has described as his efforts in securing numerous peace deals.
These include a claim that he brokered a truce between India and Pakistan - a claim India rejected.
On Thursday, Israelis and Palestinians rejoiced after a ceasefire and hostage deal was announced under a Trump initiative to end the war in Gaza.
Last week, a group of Ukrainian MPs submitted a motion asking colleagues to nominate Trump for the Nobel Prize, arguing that it was a critical show of loyalty to a strategic partner.
"If we can't show today that Ukraine and the Ukrainian parliament absolutely and totally support Donald Trump and his peace plans, then what can we talk about?" Ukrainian media quoted lawmaker Anna Skorokhod as saying on Tuesday.
Nominations for each year's Nobel prizes close on January 31.
Members of the committee can make their own nominations no later than their first meeting in February.
Kyiv is not the only government waging a charm campaign.
Taiwanese President Lai Ching-te said on Tuesday that Trump deserves the honour if he can convince China to abandon the use of force against the island.
