Italian daily newspaper Courier della Sera, citing anonymous Italian government officials, claimed the US President made the proposal to buy Italian sovereign bonds during a meeting with Italian President Giuseppe Conte at the White House last month.
One analyst said the proposal could help with any populist plans to leave the euro.
Mr Conte has so far not explained exactly what the US offer consists of and the likelihood of it ever materialising.
It comes at a time when Rome’s treasury is scheduled to issue a massive £360bon (€400bn) worth of debt in 2019.
Last year, Italy recorded a government debt equivalent to more than 130 percent of the country’s GDP but has struggled to keep repayments down due to interest lowering the effect of the European Central Bank’s asset purchase programme, which is due to end in December.
Christopher Wood, analyst of the financial letter ‘Greed and Fear’, suggested to Corriere della Sera that the US is acting as an anchor buyer of Italian bonds because Mr Trump is looking to sow deep divisions within the European Union.
He said: «The anti-euro and anti-immigration populists in Europe now have in the White House a supporter who openly encourages them to pursue their programmes.
“Trump could not have made more clear that he supports the cause of those in Italy who want to leave the euro.
“This is not unimportant because a potential future decision by the country to exit the euro may seem less risky politically and financially if it has the support of the American President.”
Italian bonds have been under increasing pressure over the past few months amid concerns over the new coalition government’s financial promises and its cooler stance towards the eurozone.
The yield on Italy’s benchmark 10-year government bonds dropped two basis points to 3.08 percent in early trading on Friday.
The benchmark had been one of the best performing in the eurozone in the first half of this week, with yields falling from 3.14 percent on Monday to lows of 2.937 percent on Wednesday.
But financial strategists have been quick to pour cold water on the news of Donald Trump’s potential offer for Italian bonds.
Christoph Rieger, head of rates strategy at German-based Commerzbank, said: «This is clearly dominating headlines this morning and it probably explains the pop at the open, but traders who look into the details of this should be quick to fade the move.
«I would be cautious though as the US has no sovereign wealth fund and neither the US Treasury nor the Fed have any mandate for such interventions.»
Matt Cairns, rates strategist at Netherlands-based Rabobank, said it was more likely that the US will look to boost investment in the Italian economy, possibly in infrastructure projects.
He added: «That would benefit from the new government’s planned, favourable tax regime aimed at boosting foreign investment in the Italian economy.”