The magazine suggests Helsinki has "breathed fresh life" into Russian sanctions
US President Donald Trump has been in the headlines this week over an apparent press conference faux pas with Russian President Vladimir Putin.
After saying he trusted Mr Putin over his own intelligence services, Mr Trump was forced to backtrack with a lesson in sentence structure.
US investigators believe Russian hackers and propaganda experts interfered in the 2016 election, in which Mr Trump beat Democrat Hillary Clinton.
But in a joint news conference with the Russian leader in Helsinki earlier this week, Mr Trump told reporters: "I have great confidence in my intelligence people but I will tell you that President Putin was extremely strong and powerful in his denial today."
Back in Washington DC on Tuesday, Mr Trump moved to clarify his remarks - insisting he never meant to say he did not see any reason why Russia would meddle in the election.
"Let me be totally clear in saying that I accept our intelligence community's conclusion that Russian meddling in the 2016 election took place - could be other people also, there's a lot of people out there. There was no collusion at all."
He added: "I realise that there is a need for some clarification. It should have been obvious - I thought it would be obvious - but I would like to clarify... in a key sentence in my remarks I said would instead of wouldn't".
"The sentence should have been 'I don't see any reason why it wouldn't be Russia'".
However Time magazine - which has featured Mr Trump several times before - has decided to focus on their relationship, merging the two men on their July 30th cover.
The composite image, by visual artist Nancy Burson, is meant to represent the men's recent meeting in Helsinki.
The magazine notes: "In addition to calling Putin’s denials 'powerful,' Trump praised the Russian as a 'good competitor' and called America itself 'foolish' for allowing the relationship between the two countries to deteriorate.
"The reaction was immediate, and as profound as what had just occurred. Trump’s infidelity to the expectations of his office as Commander in Chief left foreign-policy veterans stunned".
It adds: "Some Republicans rebuked the president. Many are loath to rein him in because they fear Trump’s popularity with GOP voters, yet even typically cautious Republicans viewed the Helsinki conference as crossing a line.
"Senate GOP leadership gave its members the green light to criticise the president.
"A bipartisan bill that would impose severe sanctions if Russia is caught meddling in 2018 or other future elections had stalled in the (US) Senate.
"Helsinki has breathed fresh life into the effort. Republican Senate aides said it could pass the chamber with even a veto-proof majority," it suggests.