JLM said its lawyers had written to the Lords Appointment Commission last month after reports that Mr Corbyn was considering recommendations for peers.
Among others, it had voiced concern about Ms Murphy at the time.
In its latest statement, it said that Mr Corbyn was “using his final weeks of office to reward failure”.
According to the ST, other nominations include the former speaker John Bercow and the former deputy Labour leader, Tom Watson, who was an outspoken critic of the party’s handling of antisemitism allegations.