The Associated Newspapers-owned title has frequently given away covermounts since 2003 and last year was giving away around one a month in an effort increase circulation.
Previous covermounts, including BBC and ITV classic dramas, are thought to have added more than 100,000 copy sales a day.
But it is thought senior executives at the newspaper believe the use of covermounts is a costly exercise, prompting a significant spike in circulation, but not luring in long-term readers.
The paper will not, however, move away from offering readers other promotional offers, such as special offers with supermarkets. It has previously teamed up with Waitrose. The Daily Mail declined to comment.
The Mail on Sunday, however, will continue to use covermounts. Last year, the MoS sold an extra 600,000 copies thanks to its promotional giveaway of Prince's new album.