The German club would prefer a loan deal and is unwilling to pay the 12 million euro asking price for the midfielder, who was sold to Tottenham for just 1.8 million last January.
A loan move is more likely this month for the 23-year-old, who is seeking regular football having started only six Premier League matches for Spurs this season.
|VIEW FROM GERMANY
|Hassan Talib Haji | Goal Germany
Holtby wants to leave to get more playing time and Schalke could be a club where he gets back the confidence he need to play at 100 percent. But the Royal Blues aren't in a position to pay the money Spurs want for him. A deal on loan is possible for both clubs.
Tottenham has told Schalke the club wants €12 million for Holtby but the Bundesliga club is deeply reluctant to offer anywhere near that amount for a player who left for just €1.8 million a year ago.
Spurs would prefer a permanent sale and will sound out interest from other clubs before sanctioning any loan deal with a view to a permanent transfer in the summer.
Holtby’s agent, Marcus Noak, confirmed earlier this week that the Germany under-21 midfielder is seeking a transfer this month.
"Lewis is desperate to play, which is why we are looking intensively for solutions," Noack told Bild. "Schalke is an interesting option."
The central midfielder is behind the likes of Mousa Dembele, Paulinho, Sandro and Nabil Bentaleb in the pecking order, while Sherwood is also understood to prefer the passing and creativity of Tom Carroll, who is currently on loan at QPR.
Sherwood is making his mark on the Tottenham squad and is also preparing to sell summer signing Etienne Capoue to Napoli, with the French midfielder also valued at around €12 million.
Jermain Defoe has signed a deal to move to MLS side Toronto at the end of February while the agent of winger Nacer Chadli, another summer signing, has expressed his client's frustration at a lack of opportunities in north London.
Holtby, who has started just once under Sherwood in Spurs' 1-1 draw with West Brom, has scored three goals in 38 appearances in all competitions for Tottenham.