Bauer said 20 jobs are "at risk" across the FHM and Zoo editorial teams and the company is consulting with employees about redundancies.
A spokesman confirmed: "The intention to suspend publication is inclusive of both the print and digital platforms for FHM and Zoo. No decision regarding the suspension will be taken until the period of consultancy has finished."
FHM was first published in 1985 as For Him Magazine and went from quarterly to monthly in 1994 and expanded with an international edition and its 100 Sexiest Women in the World poll.
Zoo’s closure follows the decision by rival publisher Time Inc UK to ax weekly counterpart, Nuts, in April 2014. Damien McSorley has been editor of Zoo since 2008.
Gareth Cherriman, the international publisher for FHM and Zoo at Bauer Media, said: "I greatly appreciate Damien McSorley’s leadership and the dedication and effort from both teams.
"I would like to thank our advertisers and retailers who have supported the brands and I’m sure that everyone who has worked on FHM and Zoo over the years will be sorry to hear this news."