A court filing also reveals that Mr Trump’s former lawyer, Michael Cohen, admitted they had discussed a potential meeting with Vladimir Putin also in 2015 after Mr Trump announced his bid to become president.
The meeting never took place because Mr Cohen was already working on a project with Russians that he believed had government contacts.
Three separate legal documents released today related to Mr Trump’s associates also say:
:: There were contacts between Mr Cohen and a Russian who offered “political synergy” on a government level in November 2015, well before previous reported contacts between the two sides.
:: The person, who claimed to be “trusted” in the Russian Federation, repeatedly asked for a meeting with Mr Trump, but the offer was not followed up.
:: They also repeatedly suggested the idea of a meeting between Mr Trump and Mr Putin, saying it could have a “phenomenal” impact “not only in political but in a business dimension as well”.
:: Mr Cohen’s activities during the 2016 presidential campaign include information about illegal payments, tax evasion and “contacts with Russian interests”.
:: Sentencing guidelines call for Mr Cohen to serve at least four years in prison – a range they said reflects his “extensive, deliberate and serious criminal conduct”.
:: Mr Trump’s former campaign manager – Paul Manafort – lied repeatedly in testimony to the Mueller investigation.
The comments from Mr Mueller’s team – which is examining allegations of Russian collusion with Mr Trump’s presidential campaign – came at the same time as prosecutors in New York filed papers saying Mr Cohen should face a “substantial prison sentence”.
Cohen had first pleaded guilty in August, confessing to evading taxes and paying the adult film actress Stormy Daniels hush money on Mr Trump’s behalf during his 2016 election campaign.
In a footnote, Mr Mueller’s team writes that Mr Cohen spoke with Mr Trump about “about contacting the Russia government before reaching out to gauge Russia’s interest in such a meeting”.
Mr Cohen also provided the special counsel’s office with details of his and others’ involvement in efforts to complete a deal to build a Trump Tower in Moscow.
However, Mr Trump responded to the revelations by tweeting: “Totally clears the President. Thank you!”
In an at times blistering note, prosecutors described Mr Cohen’s conduct as motivated by “personal greed”, saying he “sought to influence the election from the shadows” by “orchestrating secret and illegal payments” to two women.
The former lawyer has been cooperating with Mr Mueller’s investigation – giving information he reportedly hopes will lighten his sentence.
But prosecutors say he is seeking “extraordinary leniency” and have recommended that his sentence should reflect the seriousness of his “brazen violations”.
In a dramatic revelation earlier this year, Mr Cohen described how he had been directed by Mr Trump to arrange payments to buy the silence of Ms Daniels, whose real name is Stephanie Clifford, and former Playboy model Karen McDougal.
Both women alleged they had had affairs with Mr Trump.
Separate documents from the Mueller probe say that Mr Manafort met investigators on 12 separate occasions and told “multiple discernible lies” about his contacts with a Russian associate.
Mr Manafort agreed to cooperate with the inquiry in September as he pleaded guilty to two crimes related to political consulting in Ukraine.
Former national security adviser Michael Flynn has provided so much information to prosecutors that Mr Mueller this week said he shouldn’t serve any prison time.