HMG acquired the magazine three years ago, but has now concluded in the review that it is not economically feasible to continue publishing.
A consultation period for Eve, which is printed at Wyndeham Heron and currently has a circulation of 155,000, is expected to conclude some time in October.
Haymarket Consumer Media managing director Kevin Costello said: "It is with great regret that we have had to consider closing the title. They are an extremely talented group of individuals and it's a great privilege to work with them.
"Despite the valiant efforts, Eve is making an unsustainable level of loss that is exacerbated by the recent ABC decline, the continuing strength of its key competitors and uncertain conditions within the UK economy generally."
Costello has met with affected staff to inform them of the current situation.
The announcement does not affect evecars.com, however the future branding of the website is under review. Eve licensees have also been informed.
Should the magazine close, November would be the final issue.
Wyndeham Heron was unavailable for comment at this time.
Haymarket considers closing Eve magazine
Publisher Haymarket Media Group (HMG) is considering closing women's magazine title <i>Eve</i> following a review into its viability.