On Wednesday, Moscow and Washington struck a deal to hold a summit between the two leaders in a mutually convenient third country.
The US vice president told Bloomberg Mr Trump and his Russian counterpart would also discuss Moscow's involvement in the conflicts in Ukraine and Syria.
“There are a broad range of issues the president is going to talk about that need to be addressed,” Mr Pence said, including the “economic relationship with the United States and Russia and countries of the world".
Asked if they would also cover concerns over Russian interference in US elections, the vice president said: “He’s discussed that with President Putin before. I would anticipate that he will discuss that with him again.”
US intelligence officials have warned Russia will try to interfere in US congressional elections in November.
Mr Trump said the meeting would likely take place after a 11-12 July summit of Nato leaders which he is due to attend.
The US president listed Syria and Ukraine among the many subjects he said they would discuss, and he said Helsinki was a possible site for the summit.
The two men last met on the sidelines of an Asia-Pacific summit in Vietnam in November.
Afterwards, Mr Trump said he believed Mr Putin’s denials Russia had meddled in the 2016 US presidential election.
However, Mr Trump later backed away from those remarks.
Such a summit between the two leaders could irritate allies of the US, who want to isolate Mr Putin and are concerned about what they see as Mr Trump’s overly friendly attitude towards the Russian leader.
Theresa May will seek to rally European Union leaders to maintain a strong line against Russia when they meet in Brussels.
The British prime minister hopes the leaders of the 28 EU countries will back the continuation of sanctions imposed on Russia following the annexation of Crimea.
But she is also expected to stress the need for further action, including measures to tackle propaganda and the spread of disinformation by Moscow.
She will also call for action to make sure suspected spies expelled by the UK and its allies in response to the Salisbury nerve agent attack cannot simply relocate to other EU countries.
Additional reporting by agencies