The former vice president called Bennett ‘immensely talented,’ and urged him to strengthen bipartisan support of Israel.
The report added that his advisors want him to choose someone other than former Vice President Mike Pence when he does.
Trump is the first US president to be impeached twice and the first to face trial after leaving office. If convicted, the Senate could then vote to bar him from running for office again.
Vote could take place by midweek • Second Republican senator calls for resignation
Lisa Murkowski on Friday became the first Republican US senator to say Trump should resign immediately, and Republican Ben Sasse said he would "definitely consider" impeachment.
According to CNN, Pence had always planned on attending the inauguration, but had been waiting on an invitation to the event.
Vice President Mike Pence demonstrated sound leadership by coordinating defense forces to disperse the rioters and by denouncing the domestic criminals in remarks to Congress
"... the fact that you so resolutely resumed the proceedings and saw them through to their conclusion was deeply impressive and moving to all," Speaker Levin wrote.
The process concluded shortly after 3:30 am (local time) after a chaotic and violent day, in which pro-Trump supporters stormed the Capitol building.