Sources in the Labour party did not deny the claim and declined to comment on the situation.
Such a move would be remarkable given that Mr Bercow was a Tory MP, before being elevated to presiding over the main Parliamentary chamber.
Mr Bercow drew fire from a number of prominent Brexiteers over the past few years as he was accused of helping support a Remain agenda in the Commons.
It was reported that Tory high command was so angered by Mr Bercow’s stance that it took the highly unusual decision not to offer a retiring Commons speaker a place in the House of Lords.
However, Labour leader Jeremy Corbyn has stepped in and nominated Mr Bercow for a peerage, according to the Sunday Times.
ITV News Political Reporter Shehab Khan said that while it would be an "interesting move by Labour" to back a former Tory MP for a place in the Lords, "ultimately" the decision will rest with Prime Minister Boris Johnson
The newspaper also stated that Mr Corbyn had also put forward former Labour deputy leader Tom Watson, with whom he had an often tense working relationship, for a peerage.
Labour sources would not comment on any of the claims.
The newspaper said the trio appear on an eight-strong list of dissolution honours nominations put forward by the Labour chief, who will quit his post in April after leading the party to two successive general election defeats.
Vetting will begin on the nominations soon, the newspaper said.
When asked about his view on the reports, Tory Party Chairman James Cleverly told Sky's Sophy Ridge: "I'm going to fall back on convention here and by convention we don't discuss the peerages and nominations before the event.
"He's a very experienced politician."
He added: "The simple fact of the matter is the nominations process, there's always a lot of speculation, there's always good fun, until it actually comes out we won't know exactly who has been put forward and your viewers are very well informed and they can speculate all on their own.
"They don't need me to help them speculate."
International Development Secretary Alok Sharma told BBC1's The Andrew Marr Show: "I have seen that. I think that is a matter for the Labour Party. I think they are being suggested as nominating him."
Mr Corbyn’s former key aide and chief of staff Karie Murphy has also been nominated for a place in the upper house, according to the report.
But a nomination for Ms Murphy could also prove controversial given the inquiry into alleged instances of anti-Semitism in the Labour Party by the Equality and Human Rights Commission (EHRC).
The Jewish Labour Movement tweeted a statement saying Ms Murphy’s nomination was “deeply inappropriate and must be rescinded immediately”.
“Jeremy Corbyn is using his final weeks in office to reward failure,” the group added.
Labour MP, and longstanding critic of Mr Corbyn, Siobhain McDonagh, endorsed a Tweet by the group Hope Not Hate, which stated: “No one who is a subject in the EHRC investigation should be ennobled before the full EHRC report is released.”
Referring to the Tweet, Ms McDonagh said: “A very reasonable view don’t you think?”
While Labour deputy leadership contender Rosena Allin-Khan said Ms Murphy should not be nominated for a peerage until an independent inquiry into anti-Semitism is concluded.
Ms Allin-Khan told Sky's Sophy Ridge On Sunday: "What I do know is that she is currently being investigated by the Equality and Human Rights Commission (EHRC).
"Hope Not Hate said that anyone who is being investigated by the EHRC shouldn't be recommended for a peerage, so I think that does need to be taken seriously."
When asked if the nomination would make her "uncomfortable" Ms Allin-Khan said: "I would like to see the outcome of the EHRC report."