In midday trading, shares were up over 7.5 percent above $18.50 a share.
Time has asked potential buyers to submit offers by next week as the company's board of directors considers whether to sell the entire business or individual magazine titles, Bloomberg reported late Tuesday, citing sources familiar with the matter.
Five companies have expressed interest, one person told the news service. Two potential bidders include Better Homes & Gardens parent Meredith, and an investor group led by Edgar Bronfman, Jr., the report said, citing sources. At least one of the other three other bidders is a publicly traded company, the person told Bloomberg.
Bronfman is a managing partner at Accretive, an investment firm. Back in November, he made a bid for Time at $18 a share that the media company rejected. Shares of Time have soared more than 30 percent since then.
Time, the publisher of People, Time magazine and Sports Illustrated, has struggled recently, reporting lower-than-expected fourth-quarter earnings on Feb. 16.
Time, Meredith and Accretive did not immediately respond to CNBC requests for comment.
Time shares 6-month performance