A Bayer spokesman declined to comment and representatives for Schiff could not be immediately reached for comment.
While Bayer may bide its time before reacting to Reckitt's move, its management will be under pressure to salvage a deal that was well received by investors.
A bidding war cannot be ruled out. Bayer probably has to match the Reckitt offer. This would result in an acquisition price which might get unattractive for Bayer, DZ Bank analyst Peter Spengler said in a research note.
Bayer shares were 0.3 percent higher by 0815 GMT, while Reckitt dipped 0.7 percent.
Under the terms of its deal with Bayer, Schiff is allowed to entertain superior offers made in writing before Nov. 28. If it decides to go with another offer, it would have to pay a relatively modest $22 million breakup fee to Bayer.
With Schiff now in play, analysts said the situation could also attract interest from other parties - in particular Johnson & Johnson, the only other leading consumer health player lacking a presence in vitamins and supplements.
Schiff Chairman Eric Weider and private equity firm TPG Capital controlled 85 percent of the company's voting power, as of the end of October.
For Bayer, the planned acquisition of Schiff represents part of a strategy to expand into steadier, albeit less profitable, areas as a counterweight to prescription medicines, where there are high risks of clinical trial failures and patent expiries.
Reckitt, meanwhile, is keen to build up its healthcare business, which already includes painkillers, anti-acne creams and condoms. It also makes a range of household and personal care products and has brands including Durex and Cillit Bang.
Morgan Stanley & Co is acting as financial adviser to Reckitt, with Paul, Weiss, Rifkind, Wharton & Garrison LLP serving as legal adviser.