Congressional lawmakers are wrangling over Senate trial rules, with Democrats demanding witnesses be called so what they term a fair trial can take place.
Mr Trump was formally impeached by the House last week for abuse of power and obstruction of Congress.
The Senate trial is expected to begin next month, after the holiday break.
The president is accused of pressuring the Ukrainian president to start an investigation into his political rival, Democratic presidential front runner, Joe Biden.
Mr Trump is accused of doing this by withholding military aid and making a White House visit contingent on co-operation.