Oli, a free-of-charge magazine aimed at 25 to 35-year-old fashionable women, has been published since 2007. The title, which is about 700 pages per issue, is aimed at driving Oli customers to its website.
It has a distribution of about 250,000 and is mailed to existing Oli customers. It is part fee-based and part advertiser-funded.
The move could lead to redundancies at Redwood, which has five editorial staff working on the magazine. A spokesman for Oli said "the company was reviewing its paper strategy". Redwood declined to comment.
Such a move would be another blow to Redwood, after it was announced earlier this month that Homebase was axing its paid-for quarterly magazine Homebase Ideas, the last issue of which was published yesterday (Monday).