Critics interpreted the message as Baroness Harman appearing to offer the prospect of a peerage to the former council leader.
Nick Timothy, the shadow justice secretary, said it showed that Labour “will never change”.
“Fresh from the Peter Mandelson scandal, they are now trying to stuff the House of Lords with more of their cronies,” he said.
“And in this case, it seems the target is the ousted leader of Oldham council, where questions remain about the authority’s turning a blind eye to the despicable crimes of the rape gangs.
“Britain deserves better than this miserable, failing government.”
The King’s birthday honours list will be published next month. The Financial Times reported that Jim McMahon, a Labour MP and another former leader of Oldham council, is in line for a knighthood.
Oldham council was heavily criticised in a 2022 independent report into historic grooming-gang offences in the town. At the time of the report, Ms Shah was not council leader.
The review found that Greater Manchester Police and the council had failed a number of young girls who were victims of child sexual exploitation. It looked into cases from 2011 to 2014.
In February 2025, councillors in Oldham voted unanimously to demand a statutory public inquiry into child sexual exploitation in the town.
Four months later, Sir Keir Starmer announced a full statutory inquiry into grooming gangs, with Oldham one area prioritised for local investigation.
Ms Shah welcomed the inquiry, describing it as “an important step forward for our borough and for everyone who has been affected”.
She added: “We have not shied away from the issue of CSE in Oldham, we are and will continue to confront the issue without prejudice.”