The Bundesliga outfit are chasing the former Arsenal frontman as a replacement for Finnish star Teemu Pukki, who looks set to complete a move to Celtic after agreeing a €2.5 million fee with the Glasgow giants.
Adebayor, 29, is yet to feature for Andre Villas-Boas' side this season and the Portuguese tactician has made it clear that the Togo international does not feature in his first-team plans.
And Schalke are looking to hand Adebayor an exit route, with the Bundesliga side looking to add extra fire-power to their ranks.
The main stumbling block regards the structure of the deal - Tottenham want €8 million, while Schalke remain keen on bringing Adebayor in on a temporary basis, with Bild suggesting a loan move is in the offing.
With three days to go until the close of the transfer window, Schalke face a race against time if they are to bring the Spurs striker to Germany.
Meanwhile, Villas-Boas looks set to be busy dealing with incoming transfers ahead of September 2, with Vlad Chiriches, Erik Lamela and Christian Eriksen all closing in on moves to White Hart Lane.
Spurs' summer spending has already surpassed the £60 million mark, though they are likely to receive upwards of £80 million from the sale of Gareth Bale, with confirmation expected imminently.