The 19-year-old German international is regarded as one of the brightest young talents in the Bundesliga at the moment, and following a series of impressive performances in the Champions League this year, has attracted interest from the Premier League.
Red Devils boss Sir Alex Ferguson is believed to be monitoring Draxler's situation, as he contemplates a bid to bring him to Old Trafford when the transfer window reopens.
However, Manchester United will face competition for the player's signature, as Chelsea prepare a rival offer in an attempt to lure him to Stamford Bridge.
Draxler admits he is flattered to be linked with clubs as illustrious as Manchester United and Chelsea, but hinted that it is his intention to remain at the Veltins-Arena.
"I know there are offers from some of the top European clubs," Draxler is quoted by talkSPORT. "I think that is an honour. Everything is imaginable."
Schalke are currently ranked fourth in the Bundesliga table, and will need to qualify for Europe's elite club competition again next season in order to secure Draxler's long-term future.