Sane is highly rated in Germany and has been linked with a big money move away from Schalke.
Sheffield Wednesday are set to travel to Fulham at the weekend.
The Italian has no desire to head to Villa Park.
Origi limped off with a hamstring injury in the Boxing Day win over Leicester City and Jurgen Klopp updated the media on the condition of his squad.
Kyle Lafferty is said to be interested in a move to Leeds United from Norwich City.
West Ham United are set to welcome back a number of players to their first team in the coming weeks.
Crystal Palace and Leicester City are said to be interested in Fiorentina front man Khouma Babacar.
Sunderland face Aston Villa at the weekend in a basement battle in the Premier League.
Newcastle United are said to be most keen on signing Andros Townsend in January.
The Leeds star is out of contract in the summer.