In the past, Jimenez has discussed the idea of selling the Roche stake but, in an interview with Reuters three years ago, he said he would want a premium price, reflecting the difficulty of recreating such a large position in the open market.
That premium demand, however, seems to have fallen by the wayside, since Novartis is now investigating having banks collect purchase offers within a predefined price range from selected investors.
The idea of Novartis selling the stake in this way was first reported by the weekly Sonntagszeitung newspaper.
Analysts have suggested in the past that one option for unwinding the holding would be for Roche to buy the Novartis stake as part of a share repurchase program. Roche, however, has shown little interest in this idea and has traditionally viewed share buybacks as a low priority.
Roche bearer, or voting, shares slipped 0.8 percent on Monday while its most widely traded equity was off 1 percent. Novartis stock was flat.
Members of the Hoffmann-Oeri family still hold a majority of Roche's voting stock.