The call comes following reports that Bolton made claims in an unpublished book that Trump wanted to freeze aid to Ukraine unless it investigated his political rival and former Vice President Joe Biden, the BBC said in the report.
Reacting to the development on Sunday, House impeachment manager Adam Schiff, said in a tweet: "Bolton directly contradicts the heart of the President's defence. If the trial is to be fair, Senators must insist that Bolton be called as a witness, and provide his notes and other documents."
House Speaker Nancy Pelosi said that Republicans' refusal to call Bolton and others is "now even more indefensible".
There has been no comment from Bolton's lawyers, nor from the White House, according to the BBC report.
The President has previously said he does not want Bolton to testify on the grounds of national security.
Sunday's report comes after a video made public on Saturday showed Trump ordering the removal of the US ambassador to Ukraine in 2018.
With Republicans holding a 53-47 majority in the Senate, it is unlikely that the President will be removed from office.
The impeachment trial will resume in the US Senate on Monday.
Trump is charged with abuse of power and obstruction of Congress in the trial presided over by Supreme Court Chief Justice John Roberts with the senators acting as jurors.
The allegations arise from Trump's call to Ukrainian President Volodymyr Zelensky in which he asked him as a "favour" to investigate activities of Biden and his son, Hunter, in his country.
( With inputs from IANS )